How do I convert radians per second to RPM?

To convert radians per second (rad/s) to revolutions per minute (RPM), multiply the value in rad/s by 60 and divide by 2π (since 1 revolution = 2π radians and 1 minute = 60 seconds). For example, 10 rad/s equals 10 × 60 / (2π) ≈ 95.49 RPM.

What is the formula for rad/s to RPM?

The formula is: RPM = (rad/s) × 60 / (2π). This accounts for converting radians to revolutions (divide by 2π) and seconds to minutes (multiply by 60).

Why convert rad/s to RPM?

Radians per second is the SI unit for angular velocity, but RPM is more common in everyday applications like motors, engines, and rotating machinery. Converting helps in comparing specifications and understanding rotational speeds intuitively.

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计算器: Radians per Second to RPM Converter.

使用计算器: Radians per Second to RPM Converter，根据输入获得清晰实用的结果。

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输入数值

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02 / 答案

要转换的数值

Revolutions per minute (rpm)

9.549296585514

Uses rpm = radians per second × 60 ÷ (2π); direction/sign is preserved.

Cite this calculator

Canonical URL: https://mathify.one/zh/conversion/radians-per-second-to-rpm

Cite as: Mathify. (n.d.). 计算器: Radians per Second to RPM Converter. https://mathify.one/zh/conversion/radians-per-second-to-rpm

Use Cases

Motor and Engine Specifications

Compare angular velocities of motors or engines that are rated in rad/s with those rated in RPM, ensuring compatibility in design or maintenance.

Example: A motor rated at 150 rad/s converts to approximately 1432 RPM.

Physics and Engineering Calculations

Convert angular velocity values in physics problems or engineering simulations to RPM for easier interpretation or to match equipment specs.

Example: Converting 2 rad/s to RPM gives about 19.1 RPM.

Frequently Asked Questions

How do I convert radians per second to RPM?: To convert radians per second (rad/s) to revolutions per minute (RPM), multiply the value in rad/s by 60 and divide by 2π (since 1 revolution = 2π radians and 1 minute = 60 seconds). For example, 10 rad/s equals 10 × 60 / (2π) ≈ 95.49 RPM.
What is the formula for rad/s to RPM?: The formula is: RPM = (rad/s) × 60 / (2π). This accounts for converting radians to revolutions (divide by 2π) and seconds to minutes (multiply by 60).
Why convert rad/s to RPM?: Radians per second is the SI unit for angular velocity, but RPM is more common in everyday applications like motors, engines, and rotating machinery. Converting helps in comparing specifications and understanding rotational speeds intuitively.

Tips & Common Mistakes

Tips

Remember that 1 revolution equals 2π radians, so dividing by 2π is essential.
Use the conversion factor 9.5493 (which is 60/(2π)) to quickly multiply rad/s by this to get RPM.
Double-check your input units: ensure the value is truly in radians per second, not degrees per second.
For precise results, use a calculator with sufficient decimal places, especially for small values.

Common Mistakes to Avoid

Forgetting to multiply by 60 to convert seconds to minutes, leading to results that are 60 times too small.
Using 3.14 instead of 2π, which introduces a significant error; always use the full value of π.
Confusing radians per second with revolutions per second; the latter is already in revolutions, so no division by 2π is needed.

Last updated: August 13, 2026