Degrees per minute to Radian per second
°/min
rad/s
Conversion History
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Quick Reference Table (Degrees per minute to Radian per second)
| Degrees per minute (°/min) | Radian per second (rad/s) |
|---|---|
| 0.25 | 0.00007272205216643036792035615593502 |
| 0.5 | 0.0001454441043328607986725653836659 |
| 1 | 0.0002908882086657215973451307673318 |
| 6 | 0.00174532925199432945840707846039908 |
| 60 | 0.01745329251994329445840707846039908 |
| 360 | 0.10471975511965976668761061769059862 |
| 1,000 | 0.2908882086657215740973451307673318 |
About Degrees per minute (°/min)
Degrees per minute (°/min) measures slow angular rotation in a unit accessible without decimals. Clock hands move at well-known rates in °/min: the minute hand at 6°/min, the hour hand at 0.5°/min. Solar tracking mounts move at about 0.25°/min to follow the Sun across the sky. Slow geological rotations, antenna steering drives, and industrial rotary kilns are among systems where °/min is convenient. One degree per minute equals 1/60 of a degree per second.
A clock minute hand sweeps at exactly 6°/min. A solar panel tracker follows the Sun at ~0.25°/min. A slowly rotating cement kiln may turn at 1–5°/min.
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.
Degrees per minute – Frequently Asked Questions
Why does a clock minute hand move at exactly 6 degrees per minute?
A full circle is 360° and the minute hand completes it in 60 minutes: 360 ÷ 60 = 6°/min. It is one of those satisfying integer results in everyday physics. The hour hand, by contrast, moves at 0.5°/min (360° ÷ 720 minutes). At any given time, the angle between them changes at 5.5°/min — which is the key to solving those "when do the hands overlap?" puzzles.
How fast does a solar tracker panel rotate to follow the Sun?
The Sun crosses the sky at 15°/hr (360° ÷ 24 h), or 0.25°/min. A single-axis solar tracker matches this rate, adjusting continuously or in small steps throughout the day. Dual-axis trackers also compensate for the Sun's seasonal altitude change — a much slower adjustment of roughly 0.5–1° per week. The daily tracking rate of 0.25°/min is slow enough that you cannot see the panel moving.
What rotational speed in °/min do cement kilns and industrial drums operate at?
Large rotary cement kilns typically rotate at 1–5°/min (roughly 0.003–0.014 RPM). That glacial pace is intentional: raw material needs 30–60 minutes to travel the kiln's 50–100 meter length, slowly heating to 1,450°C. Faster rotation would push material through before it fully reacts. Industrial drum dryers and composting drums operate in a similar 2–10°/min range.
How do you convert degrees per minute to RPM?
Divide by 360. One full revolution is 360°, so degrees per minute ÷ 360 = RPM. The clock minute hand at 6°/min is 6/360 = 0.01667 RPM — one revolution per hour. A turntable at 33⅓ RPM is 33.33 × 360 = 12,000°/min. For rad/min, multiply °/min by π/180 ≈ 0.01745.
What °/min rate does a rotating restaurant turn at?
Most revolving restaurants complete one full rotation in 45–90 minutes, which translates to 4–8°/min. The slow rate is deliberate — fast enough that diners get a complete panoramic view during a meal, but slow enough that you do not notice the motion or feel any inertia. The famous revolving restaurant atop the BT Tower in London took about 22 minutes per revolution (16.4°/min) when it operated.
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.