The Angular Velocity Unit Converter converts between rad/s, RPM, degrees per second, and revolutions per second simultaneously. Also converts angular velocity to tangential (linear) velocity at any radius — essential for motor specs, robotics, and mechanical engineering.
1
rad/s
9.549297
RPM
0.159155
RPS
57.29578
°/s
1
m/s
6.283185
s
1
rad/s
9.549297
RPM
0.159155
RPS
57.29578
°/s
1
m/s
6.283185
s
A motor specification says 1,750 RPM. Your control system expects rad/s. The simulation wants degrees per second. The machine drawing shows rev/s. Switching between rotational speed units without error requires knowing the exact conversion factors — which is exactly what the calculator for angular velocity unit conversion provides, instantly and in all directions simultaneously.
All angular velocity units convert through radians per second as the SI base:
These factors are exact or rounded to 5 significant figures. For precision engineering, always carry sufficient decimal places — a 0.1% error in motor speed can mean a 0.1% error in machined part dimensions over a long run. Use this online calculator to convert any value among all units simultaneously. The angular velocity calculator computes ω from angle and time when it is not directly given.
One of the most useful conversions in rotational mechanics is from angular velocity to the tangential (linear) velocity at a point on the rotating object:
v = ω × r
where ω must be in rad/s and r is the radius in meters, giving v in m/s. Examples:
This conversion is critical for checking peripheral speed limits on grinding wheels, checking whether a belt drive speed is within rated range, or verifying robot joint tip speeds against safety limits.
Different industries have standardized on different angular velocity units for historical and practical reasons:
The angular acceleration calculator and physical constants and unit converters provide related mechanical and physical conversion tools.
In rotating machinery, certain angular velocities coincide with natural frequencies of the system, causing resonance — a phenomenon called critical speed. Operating near critical speed causes excessive vibration that can damage bearings, fatigue shafts, and destroy components. Knowing the exact operating speed in rad/s and comparing it to calculated natural frequencies (also in rad/s) is essential in turbine, pump, and compressor design. The separation margin — operating speed vs. critical speed — is typically required to be at least 15–20% in industrial standards such as API 670.
Select the input angular velocity unit, enter the value, and optionally enter a radius to calculate the linear speed at that radius. All conversions pass through rad/s using ω_rads = 2π × RPS = 2π × RPM/60. The period T = 2π/ω is also calculated.
Key reference: Earth rotates at 7.27 × 10⁻⁵ rad/s; vinyl records at 33.33 RPM = 3.49 rad/s; car engine idle at 800 RPM = 83.8 rad/s; centrifuge at 10,000 RPM = 1047 rad/s; fastest neutron star at 716 Hz = 4498 rad/s.
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Results
7200 RPM = 120 Hz = 754 rad/s. At disk rim (r=44mm), linear speed = 33.2 m/s = 120 km/h. Centripetal acceleration = ω²r = 754² × 0.044 = 25,000 m/s² = 2500g.
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Earth's sidereal rotation period = 86,164 s = 23h 56min 4s. Equatorial surface speed = 464.6 m/s = 1,671 km/h eastward — why rockets launch eastward to gain this free velocity.
Angular velocity ω describes rotation in space (rad/s, with a direction along the rotation axis given by the right-hand rule). Angular frequency ω = 2πf is used in oscillations and waves, with the same units (rad/s) but describing oscillatory rather than rotational motion. They are mathematically identical but conceptually distinct: a pendulum's angular frequency ω = √(g/L) describes oscillation rate, not physical rotation.
Radians per second is the SI unit and appears naturally in physical equations. In circular motion: v = ωr; centripetal acceleration a = ω²r; kinetic energy E = Iω²/2; angular momentum L = Iω; torque τ = Iα. Using RPM requires conversion factors of 2π/60 everywhere, while rad/s gives clean equations. RPM is preferred in engineering because it gives intuitive sense of rotation speed.
Millisecond pulsars are the fastest rotating compact objects known. PSR J1748-2446ad holds the record at 716 Hz = 42,960 RPM = 4498 rad/s. Its equatorial surface moves at v = ωr = 4498 × 10,000 m = 4.5 × 10⁷ m/s = 0.15c. Any faster and the centrifugal acceleration would exceed the surface gravity, tearing the star apart. This sets the absolute maximum rotation rate for neutron stars.
The Coriolis acceleration is a_Cor = -2ω × v, where ω is Earth's angular velocity vector and v is the velocity of a moving object in Earth's rotating frame. Earth's ω = 7.292 × 10⁻⁵ rad/s. The Coriolis force deflects winds rightward in the Northern Hemisphere, driving the rotation of cyclones. It also affects long-range artillery trajectories, ocean currents, and even the direction water swirls in bathtubs (though that effect is too small to dominate over initial conditions in practice).
RPM is measured by tachometers, which use: (1) optical sensors counting marks on a spinning disk; (2) magnetic Hall-effect sensors counting teeth on gears; (3) stroboscopic methods where a flashing light is tuned to the rotation frequency; (4) back-EMF measurement in electric motors. Modern car tachometers use inductive pick-ups on ignition pulses or cam/crankshaft position sensors with sub-millisecond resolution.
Angular acceleration α = dω/dt (rad/s²) is the rate of change of angular velocity. Newton's rotational second law: τ = Iα, where τ is torque and I is moment of inertia. Just as F = ma, τ = Iα. The moment of inertia I = ∫r²dm depends on mass distribution — a hollow cylinder (I = mr²) accelerates more slowly than a solid cylinder (I = mr²/2) under the same torque.
Ultracentrifuges for separating DNA, RNA, or subcellular organelles operate at 20,000-150,000 RPM (2,094-15,708 rad/s). The centrifugal acceleration a = ω²r at r = 0.05 m for 100,000 RPM: ω = 10,472 rad/s → a = 10,472² × 0.05 = 5.5 × 10⁶ m/s² = 560,000g. At this acceleration, macromolecules sediment according to the Svedberg equation based on size and density.
A spinning gyroscope resists changes to its rotation axis (gyroscopic stability). When a torque τ is applied perpendicular to the spin axis, the gyroscope precesses: the spin axis rotates at angular velocity Ω_prec = τ/(Iω), where I is moment of inertia and ω is spin angular velocity. Earth precesses around its orbit normal axis with a 25,772-year period (causing the equinoxes to precess through the zodiac).
Typical car engine ranges: idle ~700-900 RPM; city driving ~1500-3000 RPM; highway ~2000-3500 RPM; redline (gasoline) ~5000-8500 RPM; Formula 1 (peak) ~15,000 RPM. The piston in an F1 engine at 15,000 RPM completes a stroke in 2 ms; peak piston speed ~25 m/s. At redline, the crankshaft angular velocity = 15,000 × 2π/60 = 1,571 rad/s.
Reaction wheels are electrically driven spinning masses inside spacecraft. By changing the wheel's angular velocity (angular momentum), the spacecraft body must counter-rotate by the same amount (conservation of angular momentum). This provides precision attitude control without expelling propellant. The Hubble Space Telescope uses four reaction wheels, with the fourth as a spare, spinning at up to 3000 RPM with torque of ~0.1 N·m.
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