Angular Velocity Calculator
ω = Δθ / Δt = 2π·f. Conversion between rad/s, rev/min, and Hz.
Result
Angular velocity ω
314.1593 rad/s
3,000.0 RPM · 50.000 Hz.
- ω (rad/s)314.159265
- f (Hz)50.000000
- RPM3,000.0000
- deg/s18,000.0000
Step-by-step
- ω = RPM × 2π / 60 = 314.1593 rad/s.
How to use this calculator
- Pick what you have.
- Enter the value.
- Read all units.
About this calculator
Angular velocity ω measures rotation rate. ω = 2πf where f is frequency in Hz. Common conversions: 60 RPM = 1 rev/s = 2π rad/s ≈ 6.28 rad/s. Earth's rotation: ω ≈ 7.27e-5 rad/s. Engine at 6000 RPM: ω ≈ 628 rad/s. Used in physics (rotational kinematics), engineering (motor specs), navigation (gyroscopes).
Frequently asked
rad/s is SI / physics standard. RPM is engineering / consumer (motor labels). Convert: rad/s = RPM × 2π/60.
Related calculators
Centripetal Force Calculator
F_c = m × v² / r. Force required to keep object in circular motion.
Pendulum Period Calculator
T = 2π √(L/g). Period of a simple pendulum (small angles).
Torque Calculator
τ = r × F × sin(θ). Rotational force = lever arm × applied force × angle.
Vehicle Gear Ratio (Final Drive) Calculator
RPM = (MPH × 336 × ratio) / tire-diameter. Find RPM at given speed for any axle ratio.
Force Calculator (F = m·a)
Newton's second law: enter mass and acceleration, get force in newtons. Step-by-step working and pound-force conversion shown.
Work Done Calculator (W = F·d·cos θ)
Compute mechanical work from force, displacement, and the angle between them. Result in joules with calorie and foot-pound conversions.