Ah to Usable kWh Calculator – With Depth of Discharge (DoD)

This web-based tool converts between reactive power (VAR) and capacitance (µF) for both single-phase and three-phase AC systems. It supports power factor correction calculations, capacitor sizing, and electrical system commissioning. Core Formulas The calculator uses the following standard electrical engineering formulas: Single-Phase System Q (VAR) = 2π × f × C (µF) × V² × 10⁻⁶ Three-Phase System Q (VAR) = 3 × 2π × f × C (µF) × V² × 10⁻⁶ Q : Reactive power in VAR f : Frequency in Hz (typically 50 or 60 Hz) C : Capacitance in microfarads (µF) V : Voltage in volts (V) 10⁻⁶ : Conversion factor from µF to farads Input Parameters Parameter Description Reactive Power (VAR) Reactive power supplied by the capacitor, in VAR. Used to calculate required capacitance (µF). Voltage (V) - Single-phase: Phase-to-neutral voltage - Three-phase: Line-to-line (phase-to-phase) voltage Unit: Volts (V) Frequency (Hz) Number of cycles per second. Common values: 50 Hz (Europe), 60 Hz (North America). Example Calculation Single-phase system: Voltage V = 230 V Frequency f = 50 Hz Capacitance C = 40 µF Reactive power: Q = 2π × 50 × 40 × (230)² × 10⁻⁶ ≈ 6.78 kVAR Reverse calculation: Given Q = 6.78 kVAR, V = 230 V, f = 50 Hz Solve for C: C = Q / (2π × f × V² × 10⁻⁶) ≈ 40 µF Use Cases Power factor correction in industrial plants and commercial buildings Capacitor bank sizing for motor loads, transformers, and lighting circuits Electrical system commissioning and performance verification Academic learning and exam preparation in electrical engineering Energy efficiency audits to reduce utility penalties Frequently Asked Questions How do I convert VAR to µF? To convert reactive power (VAR) to capacitance (µF), use the formula: C (µF) = Q (VAR) ÷ (2π × f × V² × 10⁻⁶) For three-phase: multiply denominator by 3. Example: For 1000 VAR at 230 V, 50 Hz → C ≈ 1000 ÷ (2π × 50 × 230² × 10⁻⁶) ≈ 61.4 µF What is the difference between VAR and µF? VAR (Volt-Ampere Reactive) is a unit of reactive power — the amount of energy stored and released by capacitors or inductors. µF (microfarad) is a unit of capacitance — a physical property of the capacitor. They are related through voltage and frequency via the formula above. Can I use this calculator for three-phase systems? Yes. The calculator supports both single-phase and three-phase systems. For three-phase, select the appropriate option and input line-to-line voltage. The formula automatically multiplies by 3. Why is power factor correction important? Power factor correction improves system efficiency by reducing reactive current, which: Lowers electricity bills (reduces demand charges) Reduces losses in cables and transformers Increases available capacity in existing systems Improves voltage stability How many µF is needed for 1 kVAR? It depends on voltage and frequency. For example: At 230 V, 50 Hz: ~61.4 µF At 480 V, 60 Hz: ~14.4 µF At 240 V, 60 Hz: ~33.5 µF Use this calculator to get precise values for your system. What happens if I install too large a capacitor? Over-correction leads to overcompensation , where the power factor becomes leading (greater than 1). This can cause: Voltage rise Resonance with system inductance Damage to equipment Possible tripping of protection devices Always size capacitors based on actual load requirements. Reference Standards IEC 60831: Specifications for shunt power capacitors for AC systems IEEE 141: Recommended Practice for Electric Power Distribution for Industrial Plants NEC Article 460: Capacitors BS EN 60831: Power capacitors for AC systems

Convert delta (Δ) to wye (Y) or vice versa using the standard Δ-Y transformation formulas. Calculate equivalent resistances for circuit simplification in three-phase systems, bridge networks, and academic problems. Supports both directions with step-by-step results. Core Formulas (Δ → Y) The Δ-Y transformation preserves terminal voltages and currents while replacing the delta network with an equivalent star network: Ra = (Rab × Rbc) / (Rab + Rbc + Rac) Rb = (Rbc × Rac) / (Rab + Rbc + Rac) Rc = (Rac × Rab) / (Rab + Rbc + Rac) Where: Rab, Rbc, Rac : Resistances in the delta configuration (Ω) Ra, Rb, Rc : Equivalent resistances in the wye configuration (Ω) Reverse Formula (Y → Δ) To convert from star to delta: Rab = (Ra × Rb + Rb × Rc + Rc × Ra) / Rc Rbc = (Ra × Rb + Rb × Rc + Rc × Ra) / Ra Rac = (Ra × Rb + Rb × Rc + Rc × Ra) / Rb Input Parameters Parameter Description Rab Resistance between terminals a and b in delta configuration (Ω) Rbc Resistance between terminals b and c in delta configuration (Ω) Rac Resistance between terminals a and c in delta configuration (Ω) Example Calculation Given: Rab = 10 Ω Rbc = 20 Ω Rac = 30 Ω Calculate equivalent star resistances: Ra = (10 × 20) / (10 + 20 + 30) = 200 / 60 ≈ 3.33 Ω Rb = (20 × 30) / 60 = 600 / 60 = 10 Ω Rc = (30 × 10) / 60 = 300 / 60 = 5 Ω Result: The delta network with resistances 10 Ω, 20 Ω, 30 Ω is equivalent to a star network with Ra = 3.33 Ω, Rb = 10 Ω, Rc = 5 Ω. Use Cases Circuit simplification in complex networks with multiple loops Power system analysis for balanced and unbalanced loads Electronics design of impedance matching and filter circuits Academic learning in electrical engineering courses (e.g., Circuit Theory, Network Analysis) Exam preparation for competitive exams like GATE, IIT JAM, IEEE Frequently Asked Questions What is the difference between delta and wye connection? Delta (Δ): Three resistors connected end-to-end forming a triangle. Each resistor connects two terminals. Wye (Y): Three resistors connected at a common central node (star). Each resistor connects one terminal to the center. Both configurations can be made electrically equivalent through transformation. Why is Δ-Y transformation important? It allows engineers to simplify complex circuits by replacing a delta network with a star (or vice versa), making analysis easier using series/parallel rules or nodal/mesh methods. It’s especially useful in three-phase systems and symmetric networks. Can I use this calculator for AC circuits? Yes, but only if the components are purely resistive. For AC circuits with inductance or capacitance, you must use impedance (Z) instead of resistance (R), and the same transformation formulas apply using complex numbers. How do I convert Y to Δ? Use the reverse formulas: Rab = (Ra × Rb + Rb × Rc + Rc × Ra) / Rc Rbc = (Ra × Rb + Rb × Rc + Rc × Ra) / Ra Rac = (Ra × Rb + Rb × Rc + Rc × Ra) / Rb This calculator supports both directions: Δ → Y and Y → Δ. When should I use Δ-Y transformation? Use it when: You have a bridge-like network that cannot be simplified by series/parallel combinations You need to analyze three-phase systems with unbalanced loads You're solving problems involving symmetry or equivalence You want to reduce the number of nodes in a circuit Is Δ-Y transformation valid for all resistor values? Yes, as long as the total resistance sum (Rab + Rbc + Rac) is not zero. If any resistance is zero or infinite, special care is needed. The transformation assumes linear, time-invariant components. Reference Standards IEEE Std 145-2017: Standard for Electric Power Systems and Equipment IEC 60034: Rotating electrical machines Textbooks: "Electric Circuits" by James W. Nilsson, "Network Analysis" by M.E. Van Valkenburg Related Tools Y to Delta (Y-Δ) Conversion Three-Phase Power Calculator Impedance (Z) to Resistance (R) & Reactance (X) Mesh Current Method Solver

Convert between power units: Watt (W), Kilowatt (kW), Horsepower (HP), BTU/h, and kcal/h. Ideal for HVAC systems, motor selection, automotive engineering, and energy efficiency analysis. Includes conversion formulas, real-world examples, and support for both mechanical and metric horsepower. Supported Units & Conversion Factors Unit Full Name Relation to Watt (W) W Watt 1 W = 1 W kW Kilowatt 1 kW = 1000 W HP Horsepower - Mechanical HP: 1 HP ≈ 745.7 W - Metric HP: 1 HP ≈ 735.5 W BTU/h British Thermal Unit per hour 1 BTU/h ≈ 0.000293071 W 1 W ≈ 3.600 BTU/h kcal/h Kilocalorie per hour 1 kcal/h ≈ 1.163 W 1 W ≈ 0.8598 kcal/h Example Calculations Example 1: Air Conditioner Cooling Capacity An air conditioner has a cooling capacity of 3000 kcal/h. Power in watts: 3000 × 1.163 ≈ 3489 W Or about 3.49 kW Example 2: Engine Output Power An engine produces 200 HP (mechanical). Power in watts: 200 × 745.7 = 149,140 W Or 149.14 kW Example 3: Heating System Power A heater outputs 5 kW of power. BTU/h: 5 × 3600 = 18,000 BTU/h kcal/h: 5 × 859.8 ≈ 4299 kcal/h Use Cases Motor and generator selection based on required output power HVAC system design — sizing AC units, boilers, heat pumps Automotive engine rating — comparing horsepower and kilowatts Energy efficiency evaluation — converting between thermal and electrical power Academic learning — physics, engineering, and thermodynamics exams Frequently Asked Questions How many watts is 1 horsepower? One mechanical horsepower (HP) is approximately 745.7 watts . In metric systems, 1 HP ≈ 735.5 watts. So, 1 HP = 0.7457 kW. How do I convert kW to BTU/h? To convert kilowatts to BTU per hour: BTU/h = kW × 3600 Example: 2 kW × 3600 = 7,200 BTU/h What is the difference between mechanical and metric horsepower? Mechanical HP (US): Defined as 550 ft·lbf/s or ~745.7 W. Metric HP (PS): Defined as 75 kgf·m/s or ~735.5 W. They are slightly different but often used interchangeably in practice. How many BTU/h is 1 kW? 1 kilowatt equals 3,600 BTU/h . This is because 1 watt = 3.6 BTU/h, so 1000 watts = 3,600 BTU/h. Why is BTU/h used in HVAC systems? BTU/h (British Thermal Unit per hour) measures the amount of heat energy delivered or removed per hour. It's widely used in HVAC because it directly relates to heating and cooling performance. For example, a 12,000 BTU/h AC unit can cool a small room effectively. Can I use this calculator for electric motors? Yes. Electric motors are rated in both horsepower (HP) and kilowatts (kW). This calculator helps convert between them for comparison, selection, or efficiency analysis. Is 1 kW equal to 1 HP? No. 1 kW ≈ 1.341 HP (mechanical). So, 1 HP ≈ 0.746 kW. They are not equal, but commonly compared in industrial and automotive contexts. Reference Standards ISO 80000-13: Quantities and units — Physical chemistry and molecular physics ASHRAE Standard 90.1: Energy Standard for Buildings Except Low-Rise Residential Buildings IEEE 145-2017: Standard for Electric Power Systems and Equipment SAE J1140: Motor Vehicle Power Rating

Convert torque between Newton-metre (N·m), Kilogram-meter (kgf·m), Foot-pound (ft·lbf), and Inch-pound (in·lbf). Essential for automotive engineering, mechanical design, bolt tightening, and academic applications. Includes conversion formulas and real-world examples. Core Formula The relationship between angular velocity (ω) and frequency (f) is: ω (rad/s) = 2π × f (Hz) Or equivalently: f (Hz) = ω (rad/s) ÷ (2π) ω : Angular velocity in radians per second (rad/s) f : Frequency in Hertz (Hz) π : Pi ≈ 3.14159 Example Calculations Example 1: Motor Rotation A motor rotates at 100 rad/s. Frequency: f = 100 ÷ (2π) ≈ 15.915 Hz Rotation speed: ~15.9 revolutions per second Example 2: AC Power System Standard AC frequency is 50 Hz. Angular velocity: ω = 2π × 50 = 314.16 rad/s Used in voltage equations: V(t) = V₀ × sin(ωt) Use Cases Motor and generator design — calculating rotational speed from electrical frequency AC circuit analysis — determining angular frequency for sinusoidal signals Rotating machinery dynamics — vibration analysis, resonance studies Physics and engineering education — understanding rotational motion Control system design — feedback loops for servo motors Frequently Asked Questions How do I convert rad/s to Hz? Divide the angular velocity by 2π: f (Hz) = ω (rad/s) ÷ (2π) Example: 100 rad/s ÷ (2×3.14159) ≈ 15.915 Hz What is the difference between angular velocity and frequency? Angular velocity (ω) measures how fast an object rotates in radians per second. Frequency (f) measures how many full rotations occur per second (in Hz). They are related by: ω = 2πf. Why is angular velocity used in AC systems? In AC circuits, voltage and current vary sinusoidally over time. The rate of change is described by angular frequency (ω), which appears in the equation: V(t) = V₀ × sin(ωt). This simplifies mathematical modeling of oscillations. How many rad/s is 60 Hz? ω = 2π × 60 ≈ 376.99 rad/s This is common in North American power systems (60 Hz). Can I use this calculator for RPM? Yes, but you need to convert RPM to rad/s first: 1 RPM = 2π/60 rad/s ≈ 0.1047 rad/s Then use the calculator to find frequency. Is angular velocity the same as angular frequency? Yes, in most contexts, “angular velocity” and “angular frequency” refer to the same quantity: ω = 2πf, measured in rad/s. They describe the rate of rotation or oscillation. Reference Standards IEEE 145-2017: Standard for Electric Power Systems and Equipment ISO 80000-3: Quantities and units — Space and time Textbooks: "Engineering Mechanics" by Hibbeler, "Electric Circuits" by Nilsson