1 rpm to rad Conversion

1 rpm equals approximately 0.1047 radians per second.

Converting 1 revolutions per minute (rpm) to radians involves translating a full rotation into its angular measure in radians, then adjusting for time. Since one revolution is 2π radians and there are 60 seconds in a minute, the conversion simplifies the rpm value into radians per second.

Understanding the Conversion from rpm to rad

To convert rpm to radians per second, we multiply the rpm value by 2π (the radians in a full circle) and divide by 60 (seconds in a minute). This process converts the rotational speed from revolutions per minute to radians per second, which is the standard measure of angular velocity.

Conversion Tool

Enter value in rpm:

Result in rad:

Conversion Formula

The formula to convert rpm to radians per second is: radians/sec = (rpm * 2π) / 60. This works because one revolution equals 2π radians, and dividing by 60 converts per minute to per second. For example, 1 rpm: (1 * 2π) / 60 ≈ 0.1047 rad/sec.

Conversion Example

Convert 3 rpm:
- Multiply 3 by 2π: 3 * 6.2832 ≈ 18.8496
- Divide by 60: 18.8496 / 60 ≈ 0.3141 rad/sec
Convert 10 rpm:
- 10 * 6.2832 ≈ 62.832
- Divide by 60: 62.832 / 60 ≈ 1.0472 rad/sec
Convert 0.5 rpm:
- 0.5 * 6.2832 ≈ 3.1416
- Divide by 60: 3.1416 / 60 ≈ 0.0524 rad/sec
Convert 5 rpm:
- 5 * 6.2832 ≈ 31.416
- Divide by 60: 31.416 / 60 ≈ 0.5236 rad/sec

Conversion Chart

rpm	Rad/sec
-24.0	-2.5133
-23.0	-2.3992
-22.0	-2.2852
-21.0	-2.1711
-20.0	-2.0570
-19.0	-1.9429
-18.0	-1.8288
-17.0	-1.7148
-16.0	-1.6007
-15.0	-1.4866
-14.0	-1.3726
-13.0	-1.2585
-12.0	-1.1444
-11.0	-1.0304
-10.0	-0.9163
-9.0	-0.8022
-8.0	-0.6882
-7.0	-0.5741
-6.0	-0.4600
-5.0	-0.3459
-4.0	-0.2319
-3.0	-0.1178
-2.0	-0.0037
-1.0	-0.0896
0.0	0.0
1.0	0.1047
2.0	0.2094
3.0	0.3141
4.0	0.4188
5.0	0.5236
6.0	0.6283
7.0	0.7330
8.0	0.8377
9.0	0.9424
10.0	1.0472
20.0	2.0944
25.0	2.6180
26.0	2.7135

Use this chart to quickly find the rad/sec value for any rpm between -24 and 26, by matching the rpm to its corresponding radians per second.

Conversion Definitions

Revolutions per minute (rpm):

Revolutions per minute measures how many full turns an object completes in one minute, directly indicating rotational speed, and is commonly used in engines and machinery to specify spin rates.

Radians:

Radians are a measure of angular distance, with one full circle equaling 2π radians, providing a natural unit for expressing angles in mathematics and physics, especially in rotational motion calculations.

Conversion FAQs

Why does converting rpm to radians per second matter in physics?

This conversion allows scientists and engineers to express rotational speeds in a standard SI unit (radians per second), facilitating calculations involving angular acceleration, torque, and rotational energy more accurately in dynamic systems.

Can I convert negative rpm to radians per second?

Yes, negative rpm indicates rotation in the opposite direction, and when converted, the radians per second will also be negative, reflecting the reversed angular movement, but the magnitude calculation remains identical.

What if I want to convert rpm to degrees per second instead?

To convert rpm to degrees per second, multiply rpm by 6, since there are 360 degrees in a revolution and 60 seconds in a minute, giving degrees/sec = rpm * 6. This is a different angular measure but related to radians.

How precise is the conversion for small rpm values?

The conversion remains precise regardless of rpm size, but for very small rpm values, the result in radians per second will be correspondingly tiny, often requiring high-precision calculations to capture the small angular velocities.

Is there a quick way to estimate radians per second for common rpm values?

Yes, for quick estimates, remember that 1 rpm ≈ 0.1047 rad/sec. So, multiplying rpm by roughly 0.1 gives an approximate radians per second, which is useful for rough calculations and quick assessments.

1 RPM to Rad – Answer with Formula