Free angular velocity converter. Convert RPM (revolutions per minute) to radians per second, degrees per second, revolutions per second, and more — for motors, engines, power tools, hard drives, and physics. Instant results with strong validation.
RPM • rad/s • deg/s • rev/s
Uses the exact relationship 1 revolution = 2π radians = 360°, so RPM ↔ rad/s conversions are mathematically precise.
Perfect for engine RPM, motor specs, power-tool speeds, hard-drive RPM, and physics rotational problems.
All conversions run in your browser — no server, no account, nothing sent anywhere.
Angular velocity describes how fast something rotates. Engineers and machinists usually think in RPM (revolutions per minute), physicists work in radians per second (rad/s), and many control and graphics contexts use degrees per second (°/s). They all describe the same thing through one fixed relationship: one full revolution = 360 degrees = 2π radians (about 6.2832 radians).
The core conversions: to go from RPM to rad/s, multiply by 2π and divide by 60 (so 1 RPM = 0.10472 rad/s). To go from RPM to degrees per second, multiply by 6 (1 RPM = 6°/s, since 360° per minute ÷ 60 seconds). To go from RPM to revolutions per second, divide by 60. Reversing any of these just inverts the factor: 1 rad/s = 9.549 RPM, and 1 rev/s = 60 RPM.
Real-world reference points: a car engine idles around 600–900 RPM and redlines at 6,000–8,000 RPM. A 7,200 RPM hard drive spins 120 times every second. A typical cordless drill runs 0–1,500 RPM, an angle grinder 10,000–11,000 RPM, and a router up to 30,000 RPM. The Earth rotates once per day — about 0.0007 RPM, or 7.29 × 10⁻⁵ rad/s. A vinyl record plays at 33⅓ RPM.
Car idle: 600–900 RPM. Cruising: 2,000–2,500 RPM. Redline: 6,000–8,000 RPM. F1 engine: up to 15,000 RPM. 3,000 RPM = 314 rad/s = 50 rev/s = 18,000 °/s.
Drill: 0–1,500 RPM. Circular saw: 5,000 RPM. Angle grinder: 10,000–11,000 RPM. Router: up to 30,000 RPM. Dremel: up to 35,000 RPM.
Hard drives: 5,400 / 7,200 / 10,000 / 15,000 RPM. 7,200 RPM = 120 rev/s. Vinyl: 33⅓, 45, or 78 RPM. CD: 200–500 RPM (variable).
1 rev = 2π rad = 360°. 1 RPM = 0.10472 rad/s = 6°/s = 1/60 rev/s. 1 rad/s = 9.549 RPM. 1 rev/s = 60 RPM = 6.283 rad/s = 360°/s.
Angular velocity describes how fast something rotates, and the choice of unit reveals the discipline. Engineers and mechanics use revolutions per minute because it maps directly onto machinery; physicists use radians per second because it drops straight into the equations of rotational motion without conversion constants. The bridge between them is that one revolution is 2π radians, so RPM converts by multiplying by 2π and dividing by 60. The practical payoff is surface speed: multiply angular velocity in radians per second by radius and you get the linear speed of the rim, which is what determines cutting rates and whether a grinding wheel survives.
rad/s = RPM × 2π ÷ 60RPM = rad/s × 60 ÷ 2πSurface speed v = ω × rwhere:
Assumptions: Assumes steady rotation. The surface-speed relationship requires ω in radians per second; using RPM directly gives an answer wrong by a factor of about 9.55.
Convert an angular speed, then find how fast the edge of the wheel is actually moving.
Result3,000 RPM = 314.16 rad/s — a rim speed of 23.56 m/s
Rim speed, not RPM, is what abrasive wheels are rated for, which is why a larger wheel carries a lower maximum RPM. Fitting a large wheel to a high-speed grinder exceeds its rated surface speed and is a well-known cause of wheel burst.