Degrees Per Second to Radians Per Second Converter

How to Convert Degrees Per Second to Radians Per Second

To convert a frequency measurement from degrees per second to radians per second, divide the frequency value by the conversion factor. Since one degree per second is equal to 0.017453 radians per second, you can use this formula:

The frequency in radians per second is equal to the degrees per second divided by 57.29578.

How Many Radians Per Second Are in a Degree Per Second?

There are 0.017453 radians per second in one degree per second.

What Is a Degree Per Second?

The degree per second (symbol: °/s) is a unit of angular velocity that measures the rate of rotation in degrees of arc per second. Since one full revolution equals 360 degrees, one degree per second corresponds to 1/360 of a revolution per second (1/360 Hz). Degrees per second is commonly used in navigation, robotics, and motion sensing, where angular rates need to be expressed in the familiar degree system rather than radians. MEMS gyroscopes in smartphones, drones, and gaming controllers report angular rates in degrees per second, typically with ranges of ±250 to ±2,000 °/s. In astronomy, the rotation rates of celestial bodies are often expressed in degrees per second or degrees per hour. The Earth rotates at approximately 0.00417°/s (360° in 24 hours = 15°/hour). The Moon orbits at about 0.000152°/s. In sports science, degrees per second is used to measure joint angular velocities during movement analysis. A baseball pitcher’s shoulder internal rotation can exceed 7,000–9,000 °/s during a pitch, making it one of the fastest human movements.

One degree per second is equal to:

• 0.002778 hertz (Hz)
• 0.01745 radians per second (rad/s)
• 0.16667 revolutions per minute (RPM)
• 2.778 × 10⁻⁶ kilohertz (kHz)
• 0.002778 cycles per second (cps)

What Is a Radian Per Second?

The radian per second (symbol: rad/s) is the SI derived unit of angular velocity (rotational speed) and also serves as a unit of angular frequency. One radian per second means that the angle swept per second is one radian (approximately 57.296°). In physics and engineering, the radian per second is preferred over revolutions per minute because it simplifies mathematical equations. Angular velocity ω in rad/s is directly related to linear velocity by v = ωr and to centripetal acceleration by a = ω²r. The angular frequency ω (in rad/s) is related to the ordinary frequency f (in hertz) by ω = 2πf. This relationship appears throughout wave physics, signal processing, and electrical engineering. For example, the angular frequency of 50 Hz mains electricity is ω = 2π × 50 ≈ 314.16 rad/s. In control systems engineering, the bandwidth, natural frequency, and gain crossover frequency of systems are all expressed in radians per second. Transfer functions in the Laplace domain use s (= jω) with ω in rad/s.

One radian per second is equal to:

• 0.159155 hertz (Hz)
• 9.5493 revolutions per minute (RPM)
• 57.2958 degrees per second (°/s)
• 1.592 × 10⁻⁴ kilohertz (kHz)
• 0.159155 cycles per second (cps)

Understanding Frequency Units

Frequency is a physical quantity that measures how often a periodic event occurs per unit of time. In the most common usage, it measures the number of complete cycles of oscillation per second. Frequency is the reciprocal of the period (T): f = 1/T.

Different frequency units have evolved to serve different fields and applications. The hertz and its metric multiples dominate physics and electronics, while RPM is standard in mechanical engineering, and radians per second is preferred in mathematical physics and control theory.

Major Unit Families

• SI / Metric units: The hertz (Hz) is the SI unit of frequency, with standard metric prefixes (kHz, MHz, GHz, THz). Each prefix step is a factor of 1,000.
• Cycles per second: The cycle per second (cps) is the original name for the hertz. It is numerically identical (1 cps = 1 Hz) but predates the adoption of the “hertz” name in 1960.
• Revolutions per minute: RPM measures rotational speed and is widely used in mechanical engineering and everyday life. 1 RPM = 1/60 Hz.
• Angular velocity units: Radians per second (rad/s) and degrees per second (°/s) measure angular velocity. One full revolution = 2π rad = 360°, so 1 Hz = 2π rad/s = 360 °/s.

Frequency in Everyday Life

• Sound: Human hearing ranges from about 20 Hz to 20 kHz. Middle C on a piano is 261.6 Hz. Concert pitch A is 440 Hz.
• Electricity: Mains power alternates at 50 Hz (most of the world) or 60 Hz (Americas, parts of Asia).
• Computing: Modern CPUs run at 2–5 GHz. Monitor refresh rates are 60–360 Hz.
• Radio: AM radio: 530–1,700 kHz. FM radio: 87.5–108 MHz. Wi-Fi: 2.4 / 5 / 6 GHz.
• Rotation: Car engines idle at 600–1,000 RPM. Hard drives spin at 5,400–7,200 RPM.

Converting Between Frequency Units

All frequency units measure the same physical quantity (periodic events per unit time), so converting between them involves multiplying by the appropriate conversion factor. The key relationships are:

• 1 Hz = 1 cps (identical units)
• 1 Hz = 60 RPM (one cycle per second = 60 cycles per minute)
• 1 Hz = 2π rad/s ≈ 6.28319 rad/s (one cycle = 2π radians)
• 1 Hz = 360 °/s (one cycle = 360 degrees)

Tips for Frequency Conversions

• For SI metric conversions (Hz, kHz, MHz, GHz, THz), each prefix step is a factor of 1,000. So 1 GHz = 1,000 MHz = 1,000,000 kHz = 10⁹ Hz.
• Hertz and cycles per second are exactly the same unit (1 Hz = 1 cps). The name “hertz” was adopted in 1960 to honour Heinrich Hertz.
• To convert Hz to RPM, multiply by 60. To convert RPM to Hz, divide by 60.
• To convert Hz to rad/s, multiply by 2π (≈ 6.28319). To convert rad/s to Hz, divide by 2π.
• To convert Hz to °/s, multiply by 360. To convert °/s to Hz, divide by 360.
• To convert RPM to rad/s, multiply by 2π/60 (≈ 0.10472). This is one of the most common conversions in mechanical engineering.
• To convert RPM to °/s, multiply by 6 (since 360° ÷ 60 s = 6 °/s per RPM).
• Remember that frequency (f in Hz) and angular frequency (ω in rad/s) are related by ω = 2πf. Many physics equations use ω rather than f.

Degrees Per Second to Radians Per Second Conversion Table

The following table shows conversions from degrees per second to radians per second.

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