Radian per second to Degrees per hour
rad/s
°/h
Conversion History
| Conversion | Reuse | Delete |
|---|---|---|
| No conversion history to show. | ||
Quick Reference Table (Radian per second to Degrees per hour)
| Radian per second (rad/s) | Degrees per hour (°/h) |
|---|---|
| 0.001 | 206.2648062470963736 |
| 0.1 | 20,626.48062470963707488 |
| 1 | 206,264.8062470963708136 |
| 6.283 | 1,295,961.77765050649781984 |
| 10 | 2,062,648.062470963708136 |
| 100 | 20,626,480.6247096370812952 |
| 1,000 | 206,264,806.24709637081300384 |
About Radian per second (rad/s)
Radian per second (rad/s) is the SI unit of angular velocity, measuring how fast an angle changes over time. One full rotation (360°) equals 2π radians, so one revolution per second equals 2π rad/s ≈ 6.283 rad/s. Radian per second is the preferred unit in physics and engineering for rotational dynamics, since it makes equations involving centripetal acceleration and torque work cleanly without conversion factors. Electric motors, gyroscopes, and spinning spacecraft components are analyzed using rad/s.
Earth rotates at about 7.27 × 10⁻⁵ rad/s. A wheel spinning at 10 rad/s makes about 1.6 revolutions per second. A gyroscope precessing at 1 rad/s completes one full precession cycle in about 6.3 seconds.
About Degrees per hour (°/h)
Degrees per hour (°/h) is used for very slow angular motions, particularly in navigation, geophysics, and astronomy. High-precision gyroscopes are rated by their drift in °/h — a navigation-grade ring-laser gyro may drift less than 0.01°/h, while a consumer MEMS gyro drifts hundreds of degrees per hour. Earth's rotation corresponds to 15°/h (360° ÷ 24 h), which is why the Sun appears to move 15° per hour across the sky. Telescope drive motors use this rate to compensate for Earth's rotation during long exposures.
Earth rotates at exactly 15°/h, so astronomical telescope drives track stars at 15°/h. Navigation-grade laser gyroscopes achieve drift below 0.01°/h. The Moon moves about 0.55°/h against the background stars.
Radian per second – Frequently Asked Questions
Why do physics equations use radians per second instead of RPM or degrees?
Because radians make the maths clean. The formulas for centripetal acceleration (a = ω²r), angular momentum (L = Iω), and torque (τ = Iα) all assume ω is in rad/s. If you plug in RPM or degrees, you have to insert conversion factors of 2π/60 or π/180 everywhere. Radians are dimensionless ratios (arc length ÷ radius), so they vanish naturally from equations — no extra constants needed.
How fast does Earth rotate in radians per second?
Earth completes one full rotation (2π radians) in about 86,164 seconds (a sidereal day, slightly shorter than 24 hours). That gives approximately 7.292 × 10⁻⁵ rad/s. It sounds tiny, but at the equator it translates to a surface speed of about 465 m/s (1,674 km/h). You are always moving that fast — you just do not feel it because everything around you moves with you.
What is the difference between angular velocity and angular frequency?
They are the same number in rad/s but describe different things. Angular velocity refers to physical rotation — a wheel spinning. Angular frequency (often written ω = 2πf) describes oscillation — a vibrating spring or alternating current. A 60 Hz AC signal has ω ≈ 377 rad/s even though nothing is literally spinning. The distinction is conceptual, not mathematical.
How do you convert between rad/s and RPM?
Multiply rad/s by 60/(2π) ≈ 9.5493 to get RPM. Or divide RPM by the same factor to get rad/s. Quick shortcut: 1 rad/s ≈ 9.55 RPM, and 1,000 RPM ≈ 104.7 rad/s. If a motor spec says 3,600 RPM (common for a synchronous motor on 60 Hz mains), that is 3,600 ÷ 9.5493 ≈ 377 rad/s — the same ω as the mains frequency times 2π.
What angular velocity in rad/s does a figure skater reach during a spin?
An elite figure skater in a scratch spin pulls their arms in and reaches roughly 25–40 rad/s (about 4–6 revolutions per second). That is 240–360 RPM. The current record-holders approach 342 RPM (~35.8 rad/s). The speed increase when pulling arms in is a textbook demonstration of conservation of angular momentum — reducing the moment of inertia forces ω to increase.
Degrees per hour – Frequently Asked Questions
How fast does the International Space Station orbit in degrees per hour?
The ISS completes one orbit (360°) in about 92 minutes, giving roughly 235°/hr — almost 16 times faster than Earth's rotation. That is why astronauts see 16 sunrises every 24 hours. At an altitude of ~408 km, the station covers about 7.66 km/s of ground track. If you could watch it from a fixed point in space, it would visibly sweep through the sky at a rate where one degree takes only about 15 seconds.
Why are gyroscope drift rates measured in degrees per hour?
Because even tiny drift accumulates into serious navigation errors over a flight or voyage. A navigation-grade ring-laser gyroscope drifts less than 0.01°/hr; over a 10-hour flight that is only 0.1° of heading error. A cheap MEMS gyro drifting 10°/hr would accumulate 100° of error in the same time — useless for navigation. Expressing drift in °/hr makes the operational impact immediately obvious to a pilot or engineer.
How do telescope mounts use the 15°/hr rate for star tracking?
Equatorial telescope mounts have a motorised right-ascension axis aligned with Earth's rotation axis. By driving that axis at exactly 15°/hr (one sidereal rate), the telescope counter-rotates against Earth's spin, keeping a star fixed in the eyepiece. Without this drive, stars would drift out of view in seconds at high magnification. Astrophotographers rely on it for long exposures without star trails.
How fast does the Moon move across the sky in degrees per hour?
The Moon's apparent motion has two components. It shares the sky's overall 15°/hr westward motion due to Earth's rotation. But it also orbits Earth, moving about 0.55°/hr eastward relative to the stars (360° ÷ 27.32 days ÷ 24 hr). The net effect: the Moon moves westward across the sky at roughly 14.5°/hr, which is why moonrise occurs about 50 minutes later each day.
Why does a Foucault pendulum appear to rotate at fewer than 15°/hr at most latitudes?
A Foucault pendulum's swing plane rotates relative to the floor at 15° × sin(latitude) per hour. At the North Pole (90°) that is the full 15°/hr; at 45° latitude it is about 10.6°/hr; at the equator it is zero. The pendulum always swings in a fixed plane in inertial space — it is the Earth rotating underneath it. The sine factor comes from the fact that only the vertical component of Earth's angular velocity vector projects into the pendulum's swing plane. Paris (48.9°N) sees about 11.3°/hr, which is why Foucault's original 1851 demonstration took most of a day to complete a visible rotation.