Convert between length units: km, m, cm, mm, ft, in, mil, yd, mi, and nmi. Ideal for construction, engineering, navigation, international trade, and daily life. Supports real-time bidirectional conversion with high precision. Supported Units & Relationships Unit Full Name Description Conversion km Kilometer Used for long distances 1 km = 1000 m m Meter SI base unit of length 1 m = 100 cm = 1000 mm cm Centimeter Used for small measurements 1 cm = 10 mm mm Millimeter Used in precision machining 1 mm = 0.03937 in ft Foot Used in construction 1 ft = 0.3048 m in Inch Used for screen sizes 1 in = 2.54 cm = 25.4 mm mil Thousandth of an inch Used for wire thickness 1 mil = 0.001 in = 0.0254 mm yd Yard Used in sports fields 1 yd = 3 ft = 0.9144 m mi Statute mile Used for road distances 1 mi = 1.60934 km nmi Nautical mile Used in maritime navigation 1 nmi = 1852 m = 1.852 km Key Conversion Formulas 1 km = 1000 m 1 m = 100 cm = 1000 mm 1 ft = 0.3048 m 1 in = 2.54 cm = 25.4 mm 1 yd = 3 ft = 0.9144 m 1 mi = 1.60934 km 1 nmi = 1852 m = 1.852 km 1 mil = 0.001 in = 0.0254 mm Example Calculations Example 1: Meter to Inches 1 meter = ? inches 1 m = 100 cm → 100 ÷ 2.54 ≈ 39.37 inches Example 2: Mile to Kilometers 1 statute mile = 1.60934 km Example 3: Nautical Mile to Meters 1 nautical mile = 1852 meters Example 4: Inch to Millimeters 1 inch = 25.4 mm Example 5: Yard to Feet 1 yard = 3 feet Example 6: Millimeter to Inches 1000 mm = 1000 × 0.03937 ≈ 39.37 inches Example 7: Mil to Millimeters 1 mil = 0.0254 mm Use Cases Construction and civil engineering — converting blueprints from metric to imperial or vice versa Mechanical manufacturing and parts machining — ensuring tolerances match across global suppliers Maritime and aviation navigation — using nautical miles for sea and air routes International trade and logistics — standardizing cargo dimensions and shipping containers Teaching and student learning — understanding unit systems in math and science classes Daily life measurements — home renovation, shopping, DIY projects Frequently Asked Questions How many inches are in a meter? 1 meter = 100 centimeters. Since 1 inch = 2.54 cm, divide: 100 ÷ 2.54 ≈ 39.37 inches. What is the difference between a statute mile and a nautical mile? Statute mile = 5,280 feet = 1.60934 km — used for land distance. Nautical mile = 1,852 meters = 1.852 km — used in maritime and aviation navigation. The nautical mile is based on Earth's circumference (1 minute of latitude). Why is 1 inch equal to 25.4 mm exactly? In 1959, the US and UK agreed to define the inch as exactly 25.4 millimeters to standardize international measurements. This is now part of the international yard and pound agreement. Can I convert mils to millimeters? Yes! 1 mil = 0.001 inch = 0.0254 mm. So, multiply mils by 0.0254 to get millimeters. Example: 100 mils = 100 × 0.0254 = 2.54 mm. How do I convert feet to meters? Use the formula: meters = feet × 0.3048 Example: 10 ft × 0.3048 = 3.048 meters. Is there a difference between a yard and a meter? Yes. 1 yard = 0.9144 meters, so it's slightly shorter than a meter. A meter is about 1.0936 yards. This difference matters in precise measurements like sports field dimensions. Reference Standards ISO 80000-1: Quantities and units — Part 1: General IEC 60050: International Electrotechnical Vocabulary NIST Special Publication 811: Guide for the Use of the International System of Units (SI) Textbooks: "Engineering Mechanics" by Hibbeler, "Physics for Scientists and Engineers" by Serway

Convert between Celsius (°C), Fahrenheit (°F), and Kelvin (K) with instant results. Ideal for meteorology, engineering, science, travel, and education. Supports real-time bidirectional conversion with high precision. Supported Units & Relationships Unit Full Name Description Conversion Formula °C Degree Celsius The most widely used scale; water freezes at 0°C and boils at 100°C. - °F Degree Fahrenheit Used primarily in the United States; water freezes at 32°F and boils at 212°F. °F = (9/5) × °C + 32 K Kelvin Absolute temperature scale; 0 K is absolute zero (-273.15°C); used in physics and chemistry. K = °C + 273.15 Key Conversion Formulas °F = (9/5) × °C + 32 °C = (°F - 32) × 5/9 K = °C + 273.15 °C = K - 273.15 °F = (9/5) × (K - 273.15) + 32 Example Calculations Example 1: Human Body Temperature Normal body temperature is 37°C. °F: (9/5) × 37 + 32 = 98.6°F K: 37 + 273.15 = 310.15 K Example 2: Convert 98.6°F to °C and K 98.6°F is a typical body temperature. °C: (98.6 - 32) × 5/9 = 37°C K: 37 + 273.15 = 310.15 K Example 3: Absolute Zero 0 K is absolute zero. °C: 0 - 273.15 = -273.15°C °F: (9/5) × (-273.15) + 32 ≈ -459.67°F Example 4: Water Freezing Point Water freezes at 0°C. °F: (9/5) × 0 + 32 = 32°F K: 0 + 273.15 = 273.15 K Example 5: The Only Temperature Where °C = °F At -40 degrees: -40°C = -40°F — this is the only point where both scales read the same value. Use Cases Meteorological data interpretation — comparing weather reports from different countries Engineering design and material testing — ensuring components operate within safe temperature ranges Chemical reaction temperature control — precise lab conditions require Kelvin or Celsius Physics experiments and academic research — absolute temperature (Kelvin) is essential for thermodynamics Travel and cross-cultural communication — understanding weather forecasts in the US vs. Europe Teaching and student learning — helping students grasp unit conversion and scientific scales Frequently Asked Questions How do I convert Celsius to Fahrenheit? Use the formula: °F = (9/5) × °C + 32 Example: 20°C → (9/5) × 20 + 32 = 68°F What is the difference between Celsius and Kelvin? The Kelvin scale is an absolute temperature scale where 0 K is absolute zero (-273.15°C). To convert: K = °C + 273.15 So, 0°C = 273.15 K, and room temperature (~20°C) = 293.15 K. Why does the US use Fahrenheit instead of Celsius? Fahrenheit was developed earlier and became standardized in the US. It has finer increments (e.g., 32°F vs. 0°C), making it easier to distinguish small changes in everyday temperatures. However, most of the world uses Celsius due to its simplicity and alignment with the metric system. Can I convert directly from Fahrenheit to Kelvin? Yes! Use the formula: K = (°F - 32) × 5/9 + 273.15 Or step-by-step: first convert °F to °C, then add 273.15. Is there a quick way to estimate Celsius to Fahrenheit? Yes! A rough estimate: multiply °C by 2 and add 30. Example: 20°C → 20×2 + 30 = 70°F (actual: 68°F) This works well for weather temperatures but not for precision work. What is absolute zero in Fahrenheit? Absolute zero is 0 K = -273.15°C. Convert to Fahrenheit: (9/5) × (-273.15) + 32 ≈ -459.67°F This is the lowest possible temperature, where all molecular motion stops. Reference Standards ISO 80000-5: Quantities and units — Part 5: Thermodynamics IEC 60050: International Electrotechnical Vocabulary NIST Special Publication 811: Guide for the Use of the International System of Units (SI) Textbooks: "Thermodynamics" by Cengel & Boles, "University Physics" by Young & Freedman

Convert between digital units: bit, Byte, kB, MB, GB, and TB. Ideal for file size estimation, network speed (Mbps), storage capacity, and programming. Supports real-time bidirectional conversion with high precision. Supported Units & Relationships Unit Full Name Description Conversion b Bit The smallest unit of information, representing a binary digit (0 or 1) 1 Byte = 8 bits B Byte Basic data unit in computing, typically composed of 8 bits 1 B = 8 b kB Kilobyte 1 kB = 1024 Bytes 1 kB = 1024 B MB Megabyte 1 MB = 1024 kB 1 MB = 1,048,576 B GB Gigabyte 1 GB = 1024 MB 1 GB = 1,073,741,824 B TB Terabyte 1 TB = 1024 GB 1 TB = 1,099,511,627,776 B Key Conversion Formulas 1 Byte = 8 bits 1 kB = 1024 B 1 MB = 1024 kB = 1024² B 1 GB = 1024 MB = 1024³ B 1 TB = 1024 GB = 1024⁴ B Example Calculations Example 1: Gigabyte to Bytes 1 GB = ? Bytes 1 GB = 1024 × 1024 × 1024 = 1,073,741,824 B Example 2: Megabytes to Kilobytes 100 MB = ? kB 100 × 1024 = 102,400 kB Example 3: Bytes to Megabytes 8,388,608 B = ? MB 8,388,608 ÷ 1,048,576 = 8 MB Example 4: Terabyte to Gigabytes 1 TB = ? GB 1 TB = 1024 GB Example 5: Network Speed – Mbps to MB/s 100 Mbps = ? MB/s 100,000,000 bits/s ÷ 8 = 12.5 MB/s Note: This is why internet speeds are often advertised in Mbps but download rates show in MB/s. Use Cases File size estimation and compression — understanding how large a video or image file is Network bandwidth calculation — converting Mbps to MB/s for download speed estimates Storage device capacity comparison — comparing SSDs, HDDs, USB drives Memory analysis in programming and algorithms — estimating memory usage of data structures Data center and cloud computing resource planning — managing storage quotas and backup sizes Teaching and student learning — helping students grasp binary prefixes and data scaling Frequently Asked Questions What is the difference between bit and Byte? A bit (b) is the smallest unit of data (0 or 1). A Byte (B) consists of 8 bits. So, 1 Byte = 8 bits. For example: 1 KB = 1024 Bytes = 8192 bits. Why is 1 kB equal to 1024 Bytes, not 1000? Because computers use binary (base-2) systems. 1024 = 2¹⁰, which is close to 1000 and fits naturally in powers of two. This is known as the binary prefix. In contrast, 1000 is used in decimal (SI) prefixes like kibibyte (KiB), but most people still say "kilobyte". How do I convert Mbps to MB/s? Divide by 8 because 1 byte = 8 bits. Formula: MB/s = Mbps ÷ 8 Example: 100 Mbps ÷ 8 = 12.5 MB/s This explains why your 100 Mbps connection downloads at ~12.5 MB/s. Is there a difference between GB and GiB? Yes! - GB (gigabyte) = 10⁹ bytes = 1,000,000,000 bytes (decimal) - GiB (gibibyte) = 2³⁰ bytes = 1,073,741,824 bytes (binary) Many operating systems (like Windows) display storage in GiB, while manufacturers use GB. This causes confusion when a 1 TB drive shows only ~931 GB usable space. How many bytes are in a terabyte? 1 TB = 1024 GB = 1024 × 1024 × 1024 × 1024 B = 1,099,511,627,776 bytes That’s over 1 trillion bytes! Can this tool convert from bits to terabytes? Yes! Just input the number of bits, select the unit, and it will convert to all other units. For example: 8,796,093,022,208 bits = 1 TB (since 1 TB = 8 × 1024⁴ bits). Reference Standards ISO/IEC 80000-13: Quantities and units — Part 13: Information science IEC 60027-2: Letter symbols to be used in electrical technology NIST Special Publication 811: Guide for the Use of the International System of Units (SI) Textbooks: "Computer Systems: A Programmer's Perspective" by Bryant & O'Hallaron, "Operating System Concepts" by Silberschatz

Convert between AWG, mm², kcmil, millimeters, and inches for electrical wiring. Ideal for cable selection, power system design, electrical installations, and engineering. Supports real-time bidirectional conversion with high precision. Supported Units & Relationships Unit Full Name Description AWG American Wire Gauge A logarithmic standardized system; higher numbers indicate thinner wires. Widely used in North America. mm² Square millimeters International unit for cross-sectional area of wire. kcmil / MCM Kilo-circular mil 1 kcmil = 1000 circular mils; used for large cables like transformer leads. mm Millimeter Diameter in millimeters, useful for measurement. in Inch Diameter in inches, primarily used in North America. Key Conversion Formulas AWG → Diameter (mm): d_mm = 0.127 × 92^((36 - AWG)/39) AWG → Area (mm²): A = π/4 × d_mm² kcmil → mm²: mm² = kcmil × 0.5067 mm → in: in = mm / 25.4 in → mm: mm = in × 25.4 Example Calculations Example 1: AWG 12 → mm² Diameter ≈ 2.053 mm Area = π/4 × (2.053)² ≈ 3.31 mm² Example 2: 6 mm² → AWG Approximate AWG: 10 AWG (Actual diameter: ~2.588 mm) Example 3: 500 kcmil → mm² 500 × 0.5067 ≈ 253.35 mm² Example 4: 5 mm → Inches 5 ÷ 25.4 ≈ 0.1969 in Example 5: AWG 4 → kcmil AWG 4 has a cross-sectional area of ~21.16 mm². Convert to kcmil: 21.16 ÷ 0.5067 ≈ 417.4 kcmil Use Cases Wire and cable selection and procurement — choosing the right gauge for current load Electrical installation and wiring design — ensuring compliance with NEC or IEC standards Power system capacity calculation — determining conductor size for transformers and feeders Industrial equipment wiring standards — matching motor leads, control circuits, and busbars Electrical exams and teaching — helping students understand wire sizing and current ratings DIY electronics and PCB design — selecting appropriate jumper wires and traces Frequently Asked Questions What is AWG and how does it work? AWG stands for American Wire Gauge. It's a logarithmic scale where higher numbers mean thinner wires. For example: AWG 18 is thinner than AWG 14. Each step down (e.g., from 14 to 12) doubles the cross-sectional area. How do I convert AWG to mm²? Use the formula: d_mm = 0.127 × 92^((36 - AWG)/39) Then calculate area: A = π/4 × d_mm² Alternatively, use a lookup table or this calculator for accuracy. Why is kcmil used instead of mm² for large cables? kcmil (kilo-circular mil) is used in North America for large conductors like transformer leads and underground cables. It's based on circular mils (area of a circle with 1 mil diameter), so 1 kcmil = 1000 circular mils. This system simplifies calculations for round wires. Is there a difference between mm² and kcmil? Yes! - mm² is the metric unit of cross-sectional area. - kcmil is an imperial-based unit used in North America. Conversion: 1 kcmil = 0.5067 mm² So, 1000 kcmil ≈ 506.7 mm². Can I convert diameter in mm to AWG? Yes! Use the inverse of the AWG formula: First, find the diameter in mm. Then solve for AWG using: AWG = 36 - 39 × log₂(d_mm / 0.127) Or use this calculator for instant results. What is the largest AWG number? The largest standard AWG is AWG 40, which is very thin (~0.081 mm diameter). Smaller gauges (lower numbers) go up to AWG 0000 (4/0), which is about 11.68 mm in diameter. How do I know what wire size to use for my project? Choose based on: - **Current load** (amperage) - **Voltage drop** over distance - **Insulation type** (e.g., THHN, XHHW) - **Environmental conditions** (temperature, moisture) Refer to tables like NEC Table 310.16 or IEC 60228 for safe ampacity ratings. Reference Standards ANSI/ICEA S-73-532: Standard for Wire and Cable NEC (National Electrical Code) – Article 310: Conductors for General Wiring IEC 60228: Conductors of insulated cables UL 44: Rubber Insulated Wires and Cables Textbooks: "Electrical Engineering Principles and Applications" by Allan R. Hambley, "Handbook of Electric Power Calculation" by A. E. Fitzgerald

Calculate phase angle φ in degrees or radians and its sine, cosine, and tangent values. Ideal for AC circuit analysis, power factor calculation, motor performance evaluation, and electrical engineering education. Supports bidirectional conversion with high precision. Supported Parameters & Relationships Parameter Meaning Mathematical Relation φ (°) Phase angle in degrees Angle between voltage and current, in degrees φ (Rad) Phase angle in radians φ_rad = φ_deg × π / 180 Sin φ Sine of φ sin(φ) Cos φ Cosine of φ (Power Factor) cos(φ), i.e., Power Factor PF = P/S Tan φ Tangent of φ tan(φ) = sin(φ)/cos(φ) Key Conversion Formulas φ (rad) = φ (°) × π / 180 φ (°) = φ (rad) × 180 / π sin(φ) — sine of the phase angle cos(φ) — cosine of the phase angle; also known as Power Factor (PF) tan(φ) = sin(φ) / cos(φ) Example Calculations Example 1: Given φ = 30° φ (Rad): 30 × π / 180 ≈ 0.5236 rad sin φ: sin(30°) ≈ 0.5 cos φ: cos(30°) ≈ 0.866 (Power Factor) tan φ: tan(30°) ≈ 0.577 Example 2: Given cos φ = 0.8 φ: arccos(0.8) ≈ 36.87° φ (Rad): 36.87 × π / 180 ≈ 0.6435 rad sin φ: sin(36.87°) ≈ 0.6 tan φ: tan(36.87°) ≈ 0.75 Example 3: Given tan φ = 1.732 φ: arctan(1.732) ≈ 60° cos φ: cos(60°) = 0.5 (Power Factor) sin φ: sin(60°) ≈ 0.866 Example 4: Given φ = 90° φ (Rad): 90 × π / 180 = 1.5708 rad sin φ: sin(90°) = 1.0 cos φ: cos(90°) = 0.0 tan φ: tan(90°) → undefined (infinite) Use Cases Power system design and analysis — calculating reactive power and apparent power Motor and transformer performance evaluation — assessing efficiency and losses Power quality monitoring — detecting poor power factor and implementing correction Industrial energy efficiency optimization — reducing electricity costs via capacitors Electrical engineering exams and teaching — solving AC circuit problems Electronic circuit simulation and debugging — verifying phase relationships in filters and amplifiers Frequently Asked Questions What is the phase angle φ in an AC circuit? The phase angle φ is the angular difference between the voltage and current waveforms in an AC circuit. It indicates how much the current leads or lags the voltage. - φ = 0°: Purely resistive load (e.g., heater) - φ > 0°: Inductive load (e.g., motor, transformer) - φ < 0°: Capacitive load (e.g., capacitor bank) How is cos φ related to power factor? cos φ is the power factor (PF) in AC circuits. It represents the ratio of real power (P) to apparent power (S): PF = P / S = cos(φ) A higher cos φ means better efficiency and less wasted energy. Why is a low power factor bad? A low power factor increases current flow for the same amount of real power, leading to: - Higher I²R losses in conductors - Larger conductor sizes needed - Increased transformer and generator loading - Higher electricity bills (some utilities charge penalties) Power factor correction using capacitors can improve it. Can this tool calculate φ from sin φ or tan φ? Yes! You can input any one value: - If you know sin φ, the tool calculates φ = arcsin(sin φ) - If you know tan φ, it calculates φ = arctan(tan φ) - Then computes all other values including cos φ and φ in degrees/radians. What happens when cos φ = 0? When cos φ = 0, the phase angle φ = ±90°. This means the circuit is purely reactive (either inductive or capacitive). Real power (P) = 0, so no useful work is done. All power is reactive (Q), which oscillates between source and load. How do I interpret negative phase angles? A negative phase angle means the current leads the voltage. This occurs in capacitive loads, such as capacitor banks or certain types of electronic devices. In contrast, inductive loads (like motors) have positive φ (current lags). Is there a limit to the phase angle φ? Yes. In practical AC systems, φ typically ranges from -90° to +90°. - At ±90°, cos φ = 0 → no real power - At 0°, cos φ = 1 → maximum efficiency Most industrial systems aim for φ close to 0° (high power factor). Reference Standards IEEE 1459: Definitions for the Measurement of Electric Power and Energy IEC 61000-4-30: Power Quality Measurement NEC (National Electrical Code) – Article 450: Transformers Textbooks: "Electric Circuits" by James W. Nilsson, "Power System Analysis" by John J. Grainger

Convert between degrees-minutes-seconds (DMS), decimal degrees, radians, and grads. Ideal for GIS, navigation, mathematics, engineering, and astronomy. Supports real-time bidirectional conversion with high precision. Supported Units & Conversion Factors Unit Full Name Relation to Degree (°) DMS Degrees-Minutes-Seconds 1° = 60′, 1′ = 60″ Example: `90° 20′ 30″ = 90 + 20/60 + 30/3600 ≈ 90.3417°` Decimal Degree Decimal Degrees 1° = 1° (direct representation) Rad Radian 1 rad = 180° / π ≈ 57.2958° 1° = π / 180 ≈ 0.017453 rad Grad Grad (or Gon) 1 grad = 0.9° 1° = 100 centesimal minutes 1 grad = 100 centesimal seconds Example: `100 grad = 90°` Key Conversion Formulas DMS → Decimal Degrees: Decimal° = Degrees + Minutes/60 + Seconds/3600 Decimal Degrees → Radians: rad = ° × π / 180 Radians → Decimal Degrees: ° = rad × 180 / π Decimal Degrees → Grads: grad = ° × 100 / 90 = ° × 1.111... Grads → Decimal Degrees: ° = grad × 0.9 Example Calculations Example 1: DMS to Decimal Degrees Input: `90° 20′ 30″` Calculation: 90 + 20/60 + 30/3600 = 90 + 0.3333 + 0.008333 ≈ 90.3417° Example 2: Decimal Degrees to Radians Input: `90.3417°` Calculation: 90.3417 × π / 180 ≈ 1.5768 rad Example 3: Radians to Grads Input: `π/2 rad ≈ 1.5708 rad` Step 1: Convert to degrees: 1.5708 × 180 / π ≈ 90° Step 2: Convert to grads: 90° × 100 / 90 = 100 grad So: `π/2 rad = 100 grad` Example 4: Grads to DMS Input: `123.4 grad` Step 1: Convert to degrees: 123.4 × 0.9 = 111.06° Step 2: Convert to DMS: - Degrees: 111° - Minutes: 0.06 × 60 = 3.6′ → 3′ 36″ Result: 111° 3′ 36″ Example 5: Common Angles Reference Table Degrees Radians Grads 0° 0 0 15° π/12 16.66 30° π/6 33.33 45° π/4 50 60° π/3 66.66 90° π/2 100 180° π 200 360° 2π 400 Use Cases Geographic Information Systems (GIS) and map coordinates — converting latitude/longitude from DMS to decimal Navigation and aviation positioning — GPS data often uses decimal degrees Mathematics education and trigonometric calculations — teaching students how to convert between systems Robotics motion control — angular position sensors may output in radians or degrees Astronomy and timekeeping — celestial coordinates use DMS format Engineering drawing and mechanical design — CAD software may require specific angle formats Frequently Asked Questions What is the difference between degrees and grads? Degrees divide a circle into 360 parts. Grads (or gons) divide a circle into 400 parts, so 1 grad = 0.9°. This system was designed to simplify calculations in surveying and civil engineering. Why do we use DMS format in geography? DMS (Degrees-Minutes-Seconds) is traditional in cartography and navigation because it allows precise location representation. For example: `40° 42′ 51″ N, 74° 0′ 21″ W` is New York City's coordinates. It’s especially useful when high precision is needed. How do I convert DMS to decimal degrees? Use the formula: Decimal° = Degrees + Minutes/60 + Seconds/3600 Example: `30° 15′ 30″` = 30 + 15/60 + 30/3600 = 30.2583° Can this tool handle negative angles? Yes! Negative angles represent clockwise rotation from the positive x-axis. They are commonly used in navigation and robotics. For example: `-45°` = 315° in standard position. What is the relationship between radians and degrees? One full circle is: - 360° in degrees - 2π radians ≈ 6.2832 rad So: 1 rad = 180° / π ≈ 57.2958° And: 1° = π / 180 ≈ 0.017453 rad Is there a limit to the angle values? No practical limit. Angles can be any real number. However, most applications normalize angles to the range [0°, 360°) or [-180°, 180°]. For example: 400° = 40° (mod 360°). Reference Standards ISO 19111: Geographic information — Spatial reference systems WGS84: World Geodetic System 1984 (used by GPS) IEC 60050: International Electrotechnical Vocabulary Textbooks: "Calculus" by James Stewart, "Surveying Principles and Applications" by Charles D. Ghilani

Convert between common pressure units: bar, Pa, kPa, MPa, atm, psi, mmHg, inHg, mmH₂O, inH₂O, N/cm², and kg/cm². Ideal for engineering, meteorology, medical devices, HVAC systems, and academic learning. Supports real-time bidirectional conversion with high precision. Supported Units & Conversion Factors Unit Full Name Relation to Pascal (Pa) bar Bar 1 bar = 100,000 Pa Pa Pascal 1 Pa = 1 N/m² hPa Hectopascal 1 hPa = 100 Pa kPa Kilopascal 1 kPa = 1,000 Pa MPa Megapascal 1 MPa = 1,000,000 Pa atm Atmosphere 1 atm ≈ 101,325 Pa N/cm² Newton per square centimeter 1 N/cm² = 10,000 Pa kg/cm² Kilogram per square centimeter 1 kg/cm² ≈ 98,066.5 Pa psi Pound per square inch 1 psi ≈ 6,894.76 Pa psf Pound per square foot 1 psf ≈ 47.8803 Pa mmH₂O Millimeter of water 1 mmH₂O ≈ 9.80665 Pa inH₂O Inch of water 1 inH₂O ≈ 249.089 Pa mmHg Millimeter of mercury 1 mmHg ≈ 133.322 Pa inHg Inch of mercury 1 inHg ≈ 3,386.39 Pa Key Conversion Formulas bar → Pa: Pa = bar × 100,000 kPa → Pa: Pa = kPa × 1,000 MPa → Pa: Pa = MPa × 1,000,000 atm → Pa: Pa = atm × 101,325 psi → Pa: Pa = psi × 6,894.76 mmHg → Pa: Pa = mmHg × 133.322 inHg → Pa: Pa = inHg × 3,386.39 mmH₂O → Pa: Pa = mmH₂O × 9.80665 inH₂O → Pa: Pa = inH₂O × 249.089 N/cm² → Pa: Pa = N/cm² × 10,000 kg/cm² → Pa: Pa = kg/cm² × 98,066.5 Example Calculations Example 1: Car Tire Pressure (30 psi) kPa: 30 × 6.895 ≈ 206.85 kPa bar: 206.85 / 100 ≈ 2.07 bar atm: 206.85 / 101.325 ≈ 2.04 atm Example 2: Blood Pressure (120 mmHg) Pa: 120 × 133.322 ≈ 15,998.6 Pa kPa: 15.9986 kPa psi: 15.9986 / 6.895 ≈ 2.32 psi Example 3: HVAC Duct Static Pressure (200 Pa) mmH₂O: 200 / 9.80665 ≈ 20.4 mmH₂O inH₂O: 20.4 / 25.4 ≈ 0.80 inH₂O hPa: 200 / 100 = 2 hPa Example 4: Atmospheric Pressure (1 atm) Pa: 1 × 101,325 = 101,325 Pa bar: 101,325 / 100,000 ≈ 1.01325 bar mmHg: 101,325 / 133.322 ≈ 760 mmHg Example 5: Vacuum Gauge Reading (10 inHg) Pa: 10 × 3,386.39 = 33,863.9 Pa psi: 33,863.9 / 6,894.76 ≈ 4.91 psi atm: 33,863.9 / 101,325 ≈ 0.334 atm Use Cases Hydraulic and pneumatic system design — selecting pumps, valves, and cylinders Tire pressure regulation — ensuring optimal vehicle performance and safety Medical devices — blood pressure monitors, ventilators, infusion pumps Meteorology and weather forecasting — atmospheric pressure in hPa or mmHg Vacuum technology and sensor calibration — low-pressure environments Academic learning and exams — physics, engineering, and chemistry courses Frequently Asked Questions What is the difference between bar and atm? bar is a metric unit where 1 bar = 100,000 Pa. atm (standard atmosphere) is based on Earth's sea-level pressure: 1 atm ≈ 101,325 Pa. So: 1 atm ≈ 1.01325 bar. They are close but not equal. Why is mmHg used in blood pressure measurement? mmHg (millimeters of mercury) is traditional because early sphygmomanometers used mercury columns. It’s still used today due to historical standardization and precision. Normal blood pressure is around 120/80 mmHg. How do I convert psi to bar? Use the formula: bar = psi × 0.06895 Example: 30 psi × 0.06895 ≈ 2.07 bar Can this tool handle negative pressures? Yes! Negative pressures represent vacuum or sub-atmospheric conditions. For example: -10 kPa means 10 kPa below atmospheric pressure. Common in HVAC, vacuum pumps, and medical suction devices. What is the relationship between kg/cm² and bar? 1 kg/cm² ≈ 98,066.5 Pa 1 bar = 100,000 Pa So: 1 kg/cm² ≈ 0.980665 bar And: 1 bar ≈ 1.0197 kg/cm² Is there a limit to the pressure values? No practical limit. The calculator handles very small (e.g., micro-Pa) and very large (e.g., GPa) values. However, most applications use typical ranges: - Atmosphere: 100–101,325 Pa - Tire: 200–300 kPa - Medical: 0–300 mmHg - Industrial: 1–100 MPa Reference Standards ISO 13448: Measurement of pressure ASTM E2228: Standard Specification for Pressure Transducers IEC 60050: International Electrotechnical Vocabulary Textbooks: "Fluid Mechanics" by Frank M. White, "Engineering Thermodynamics" by Cengel & Boles

Calculate accurate battery runtime using Peukert effect, depth of discharge (DoD), and series/parallel configurations. Supports lead-acid, AGM, gel, and lithium-ion for solar, EV, UPS, and off-grid systems. This tool estimates the theoretical runtime of a battery under a given load by considering configuration, capacity, discharge rate, and battery chemistry. Ideal for off-grid systems, backup power, electric vehicles, and portable electronics. How Do You Calculate Battery Runtime? The basic formula is: Runtime (hours) = (Total Capacity × DoD) / Load Current Where: - Total Capacity = Number of Batteries × Capacity per Battery × Connection Factor - DoD = Depth of Discharge (% or Ah) - Load Current = Load Power / Voltage (if in watts) Peukert Equation for Realistic Runtime The accurate runtime is calculated using: t = (C₀ × Tᵏ) / Iᵏ Where: t = Actual runtime (hours) C₀ = Rated capacity of a single battery (Ah, e.g., 100 Ah @ 20h) T = Rated discharge time (hours, typically 20 h for lead-acid) I = Total load current (A) = Load Power (W) / System Voltage (V) k = Peukert constant (see table below) Note: For multi-battery systems, total capacity and voltage are first computed based on series/parallel configuration before applying this formula. What Is the Peukert Effect and How Does It Affect Battery Life? The Peukert effect describes how battery capacity decreases as discharge rate increases. Higher currents reduce usable capacity, especially in lead-acid batteries. Peukert constant (k) > 1.0 indicates capacity loss at high rates Lithium-ion batteries have k ≈ 1.0 → less affected Older batteries have higher k values due to internal resistance increase This calculator uses the Peukert equation to provide more accurate runtime estimates than simple division. How Does Battery Connection (Series vs Parallel) Affect Runtime? Battery connections change total voltage and capacity: Series: Voltages add up, capacity stays the same → higher voltage, same runtime Parallel: Voltage stays the same, capacities add up → same voltage, longer runtime Series-Parallel: Combines both effects → higher voltage and longer runtime Example: Two 12V 100Ah batteries in parallel = 12V 200Ah → doubles runtime. What Is Depth of Discharge (DoD) and Why Is It Important? Depth of Discharge (DoD) is the percentage of battery capacity used during a cycle: DoD = (Used Capacity / Total Capacity) × 100% Higher DoD = longer runtime but shorter battery lifespan Lead-acid: typically limited to 50% DoD to extend cycle life Lithium-ion: can safely reach 80–100% DoD Exceeding recommended DoD reduces battery health and performance Always consider manufacturer recommendations for optimal battery longevity. How Does Battery Age Affect Runtime? As batteries age, their internal resistance increases and capacity degrades: Capacity drops by 10–20% per year in lead-acid batteries Peukert constant increases with age → faster capacity loss at high loads Efficiency decreases → more energy lost as heat This calculator assumes new battery conditions. For aged batteries, reduce rated capacity by 10–20% for realistic estimates. Can I Use This Calculator for Lithium-Ion Batteries? Yes! The calculator supports all battery types, including lithium-ion: Use Peukert constant ≈ 1.0–1.28 (closer to 1.0 than lead-acid) Allow higher DoD (up to 100%) without significant damage Less sensitive to discharge rate → Peukert effect is minimal However, always check manufacturer specs for temperature limits and charge/discharge cycles. Parameter Description Parameter Description Connection Select battery configuration: • Series: Voltages add, capacity unchanged • Parallel: Voltage unchanged, capacities add • Single: One battery Number of Batteries Total number of batteries in the system. Voltage (V) Nominal voltage of a single battery (e.g., 12V, 24V). Capacity (Ah) Rated capacity of a single battery in ampere-hours (Ah). Load (W or A) Power consumption of connected device: • In watts (W): suitable for most appliances • In amperes (A): when operating current is known Peukert Constant (k) Coefficient for capacity correction at different discharge rates: • Lead-Acid: 1.1–1.3 • Gel: 1.1–1.25 • Flooded: 1.2–1.5 • Lithium-Ion: 1.0–1.28 Depth of Discharge (DoD) Percentage of capacity discharged relative to full charge. • Can be entered as % or Ah • Typical values: 50% (lead-acid), 80–100% (lithium-ion) Rated Discharge Time Time (in hours) over which the rated capacity is measured (usually 20h for lead-acid). Battery Runtime Calculation Principle The calculator uses the following steps: Compute total system voltage and capacity based on connection type Apply Peukert equation to correct capacity for actual discharge rate Calculate available energy: E = V × C × DoD Divide by load power to get runtime: t = E / P For DC systems, efficiency is assumed 100%. Real-world losses (wires, inverters) may reduce actual runtime by 10–20%. Usage Recommendations Use for sizing UPS, solar systems, EVs, and portable power stations Consider safety margins: multiply runtime by 0.8–0.9 for real-world conditions Limit DoD to preserve battery life (especially for lead-acid) Account for temperature effects: cold reduces capacity by 20–30% Regularly recalibrate based on observed performance This calculator adheres to IEEE standards and supports accurate battery runtime estimation in real-world applications.

Calculate missing transformer parameter: input any 3 of primary/secondary voltage (Vp, Vs) or turns (Np, Ns). Ideal for step-down/up design. Free, no signup. Instantly solve for any missing value—primary voltage (Vp), secondary voltage (Vs), primary turns (Np), or secondary turns (Ns)—using the ideal transformer equation. Just enter any three known quantities, and the tool calculates the fourth in real time—no manual algebra, no guesswork. Formula & Working Principle Fundamental Transformer Equation All calculations are based on the ideal transformer model, governed by the turns ratio law: Vp / Vs = Np / Ns Where: Vp = Primary voltage (AC input, in volts) Vs = Secondary voltage (AC output, in volts) Np = Number of turns in the primary winding Ns = Number of turns in the secondary winding Key Assumptions This calculator assumes an ideal transformer, meaning: No core losses (hysteresis or eddy currents) No copper losses (winding resistance = 0) No leakage flux (perfect magnetic coupling) No magnetizing current These simplifications are standard in design-phase estimation, where quick parametric validation is more critical than real-world efficiency modeling. For detailed performance analysis, use finite-element simulation tools. How It Works The equation can be rearranged to solve for any unknown: Vp = Vs * (Np / Ns) Vs = Vp * (Ns / Np) Np = Ns * (Vp / Vs) Ns = Np * (Vs / Vp) Our tool automates this logic—you just input three values. Practical Example Scenario: You’re designing a step-down transformer to convert a 480 V industrial supply to 120 V for control circuitry. The primary winding will have 800 turns. How many secondary turns are needed? Given: Vp = 480 V Vs = 120 V Np = 800 Calculation: Ns = Np * (Vs / Vp) = 800 * (120 / 480) = 800 * 0.25 = 200 Result: 200 secondary turns are required. This exact calculation takes one second in the tool—just enter the three known values and get the answer instantly. Common Applications Step-Down Transformer Design Convert 480 V to 120 V for control circuits. Input Vp, Vs, Np → get Ns. Step-Up Transformer Sizing Build a 12 V to 240 V inverter stage. Input Vp, Vs, Ns → get Np. Isolation Transformer Specification Verify 1:1 ratio (e.g., Vp = Vs = 230 V → Np = Ns). Rapid Prototyping & BOM Estimation Estimate wire length and layer count from calculated turns for mechanical integration. Educational Validation Students and instructors verify homework or lab results instantly. Who Is This For? This tool is designed for professionals who need fast, reliable transformer parameter estimation during the conceptual or specification phase: Electrical Engineers – Designing power supplies, motor drives, or distribution systems Power System Designers – Specifying transformers for industrial or utility applications Industrial Equipment Architects – Integrating custom magnetics into machinery R&D Engineers – Prototyping new energy conversion topologies Technical Educators & Students – Teaching or learning transformer fundamentals Note: This tool is not intended for final production validation, where thermal, efficiency, and regulatory compliance must be modeled with advanced simulation software. Frequently Asked Questions What is the formula for transformer winding? The core formula is Vp / Vs = Np / Ns. This relates input/output voltages to the number of turns in each coil. How do you calculate transformer turns? Enter any three of: primary voltage, secondary voltage, primary turns, or secondary turns. The calculator solves for the missing value using the ideal transformer equation. Can a transformer go from 120V to 240V? Yes—that’s a step-up transformer with a 1:2 turns ratio. For example, 100 primary turns require 200 secondary turns. How to find secondary turns from voltage? Use Ns = Np * (Vs / Vp). Our calculator does this automatically when you input Vp, Vs, and Np. What does “ideal transformer” mean? An ideal transformer has no losses (no resistance, no core loss, perfect coupling). It’s used for theoretical design estimates, not real-world efficiency prediction. Is this calculator accurate for real transformers? It’s accurate for initial sizing and ratio validation. Real transformers require derating for losses, regulation, and temperature—but this tool gives you the correct starting point. Do I need to sign up to use it? No. The calculator is free, requires no email, and works instantly on any device.

Calculate heat energy (joules) dissipated in resistors using Joule's Law: Q = I²Rt. Essential for circuit design, thermal safety, and power loss analysis in electrical systems. This tool calculates the heat energy (Q) dissipated as thermal energy in resistive elements of an electrical circuit using Joule’s Law. Essential for thermal management, component selection, and fire risk prevention in electronics and power systems. What Is Joule’s Law of Heating? Joule’s Law states that the heat energy generated in a resistor is directly proportional to: The square of the current (I²) The resistance (R) The time the current flows (t) The formula is: Q = I² × R × t Alternatively, since power P = I²R, we can also write: Q = P × t Where: Q = Heat energy (joules, J) I = Current (amperes, A) R = Resistance (ohms, Ω) t = Time (seconds, s) P = Power (watts, W) How Do You Calculate Heat Energy from Current and Resistance? Use Q = I² × R × t when you know: Current flowing through the resistor Resistance value Duration of current flow Example: I = 2 A, R = 10 Ω, t = 5 s → Q = (2)² × 10 × 5 = 200 J Why Does a Resistor Get Hot When Current Flows Through It? As electrons move through a resistive material: They collide with atoms in the lattice Kinetic energy is converted into vibrational energy This manifests as heat (thermal energy) This process is irreversible — electrical energy is permanently lost as heat. Is Heat Proportional to Current or Current Squared? Heat is proportional to the square of the current. This means: Doubling current → 4× more heat Tripling current → 9× more heat This quadratic relationship makes overcurrent a major cause of overheating and component failure. What Is the Unit of Heat Energy in Circuits? The SI unit is the joule (J). Since 1 watt = 1 joule/second: A 1W resistor running for 1 second dissipates 1 J For larger systems, kilojoules (kJ) or watt-hours (Wh) may be used How Is Power Related to Heat Dissipation? Electrical power consumed by a resistor is entirely converted into heat: P = I²R = V²/R = VI Therefore, total heat energy over time is simply: Q = P × t This is why power rating (e.g., ¼W, 1W, 5W) is critical when selecting resistors. Parameter Definitions Parameter Description Resistance (R) Opposition to current flow, measured in ohms (Ω). Higher R → more heat for same current. Example: 100 Ω resistor limits current and generates heat. Current (I) Flow of electric charge, in amperes (A). Heat ∝ I² — doubling current quadruples heat! Example: 1 A vs. 2 A → 4× more heat. Power (P) Rate of energy conversion, in watts (W). 1 W = 1 J/s. Can be calculated as P = I²R or P = V × I. Example: A 5W LED dissipates 5 J every second. Time (t) Duration of current flow, in seconds (s). Longer time → more total heat. Example: 60 s produces 60× more heat than 1 s. Application Scenarios Designing heating elements (e.g., electric stoves, hair dryers, space heaters) Estimating power loss in transmission lines and connectors Predicting temperature rise in PCB traces, ICs, and resistors Selecting resistors with adequate power ratings to avoid burnout Performing safety analysis to prevent overheating and fire hazards Understanding thermal behavior in battery packs and motor windings Important Notes This model assumes all electrical energy is converted to heat (ideal resistor) For AC circuits, use RMS current values in the formula Always include a safety margin (e.g., operate at ≤70% of max power rating) This calculator adheres to fundamental principles of electromagnetism and thermodynamics, providing reliable estimates for educational and engineering purposes.