Degrees per hour to Cycle per second
°/h
cps
Conversion History
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|---|---|---|
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Quick Reference Table (Degrees per hour to Cycle per second)
| Degrees per hour (°/h) | Cycle per second (cps) |
|---|---|
| 0.001 | 0.00000000077160493827 |
| 0.01 | 0.00000000771604938272 |
| 0.55 | 0.00000042438271604938 |
| 6 | 0.00000462962962962963 |
| 15 | 0.00001157407407407407 |
| 360 | 0.00027777777777777778 |
| 3,600 | 0.00277777777777777778 |
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.
About Cycle per second (cps)
Cycle per second (cps) is the older, pre-SI term for what is now called hertz. One cycle per second equals exactly one hertz. The term was in common use through the mid-20th century in electrical engineering and acoustics — specifications for audio equipment, radio equipment, and mains electricity were all stated in cycles per second. The SI formally replaced "cycles per second" with "hertz" in 1960, and the change was widely adopted through the 1960s–70s. Some older technical literature and vintage equipment datasheets still use cps.
A 1950s amplifier spec sheet listing "frequency response 20–20,000 cps" means the same as 20 Hz–20 kHz. The US mains supply was described as "60 cps" before 1960.
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.
Cycle per second – Frequently Asked Questions
Why did the SI replace "cycles per second" with "hertz" in 1960?
The General Conference on Weights and Measures wanted consistent named units honoring key physicists, paralleling the watt, volt, and ampere. "Cycles per second" was descriptive but wordy, and it didn't follow the pattern of one-word unit names. Heinrich Hertz — who proved electromagnetic waves exist — was the obvious namesake. The swap was official from 1960, though many engineers kept saying "cps" well into the 1970s.
Are there any situations where "cycles per second" is still preferred over hertz?
In some vintage audio and ham radio communities, "cps" persists as nostalgic shorthand. More practically, it survives in teaching contexts where making the physical meaning explicit is helpful — telling a student that 440 cps means "440 complete vibrations each second" is more intuitive than "440 Hz" until they have internalised the unit. Officially, though, every standards body has switched to hertz.
If cycles per second and hertz are identical, why does this converter page exist?
Because people searching for "cycles per second to hertz" are usually reading an old textbook or datasheet that uses cps and want confirmation that it is a 1:1 equivalence — no multiplication needed. The conversion factor is exactly 1, but verifying that still saves someone a trip to the library or a forum post.
What did equipment spec sheets look like before hertz was adopted?
A 1950s oscilloscope might list its bandwidth as "DC to 5,000,000 cps." A radio receiver would specify "tuning range: 540 to 1,600 kc/s" (kilocycles per second). Turntable specs read "wow and flutter: 0.15% at 33⅓ cps." After 1960, "kc/s" became "kHz" and "Mc/s" became "MHz," but the underlying numbers stayed identical.
How is "cycles per second" different from "radians per second"?
One cycle is one full oscillation — from peak to peak. One radian is about 1/6.28 of a full circle. So 1 cycle per second = 2π radians per second ≈ 6.283 rad/s. Engineers use radians per second in equations where angular measure matters (torque, rotational inertia), and cycles per second (hertz) when counting whole oscillations. Forgetting the 2π factor is one of the most common mistakes in physics homework.