RPM = (60 * ω) / (2 * π)
ω = (RPM / 60) * 2 * π
ω = mps / r
mps = r * ω
RPM = Rotational speed (revolutions/minute)
ω = Angular velocity (rad/s)
mps = Speed (m/s)
r = Radius (m)
π = 3.1415926535
A tool for converting between angular velocity (RPM, rad/s) and linear velocity (m/s, ft/s), with support for radius to enable precise calculations.
This converter supports:
Input RPM → automatically calculate rad/s, m/s, ft/s
Input rad/s → automatically calculate RPM, m/s, ft/s
Input m/s or ft/s → reverse-calculate RPM and rad/s using radius
Real-time bidirectional calculation without manual switching
ω (rad/s) = (2π / 60) × RPM
RPM = (60 / 2π) × ω
v (m/s) = ω × r
v (ft/s) = v (m/s) × 3.28084
Motor speed is 3000 RPM, find angular velocity → ω = (2π / 60) × 3000 ≈ 314.16 rad/s
Angular velocity is 100 rad/s, find RPM → RPM = (60 / 2π) × 100 ≈ 954.93 RPM
Wheel radius is 0.1 m, angular velocity is 100 rad/s, find linear velocity → v = 100 × 0.1 = 10 m/s
Linear velocity is 10 m/s, convert to ft/s → 10 × 3.28084 ≈ 32.81 ft/s
Motor and generator selection
Car tire RPM to speed conversion
Wind turbines, pumps, fans design
Robot joint control and motion planning
Physics education: circular motion, centripetal acceleration
RPM stands for revolutions per minute, and rad/s stands for radians per second. The conversion formula is: ω = (2π / 60) × RPM, meaning 1 RPM ≈ 0.1047 rad/s. For example, 3000 RPM corresponds to approximately 314.16 rad/s.
Linear velocity v = ω × r, meaning linear velocity equals angular velocity multiplied by radius. At the same rotational speed, a larger radius results in a higher linear velocity. Therefore, the radius of the rotating body must be known to accurately calculate RPM from linear velocity.
1 meter = 3.28084 feet, so v(ft/s) = v(m/s) × 3.28084. For example, 10 m/s ≈ 32.81 ft/s. For reverse conversion, divide by 3.28084.
It is commonly used for motor selection (RPM and angular velocity conversion), car tire RPM to speed conversion, blade linear velocity calculation for fans, pumps, and wind turbines, robot joint motion planning, and learning about circular motion and centripetal acceleration in physics education.
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