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1 rpm equals approximately 0.1047 radians per second.
Converting revolutions per minute (rpm) to radians involve understanding that one revolution is 2π radians, and converting minutes to seconds. So, 1 rpm means one full turn each minute, which is 2π radians divided by 60 seconds, resulting in about 0.1047 rad/sec.
Conversion Result
When you convert 1 rpm into radians, you get roughly 0.1047 radians per second. This means that rotating at 1 revolution per minute is equivalent to spinning about 0.1047 radians every second.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is: radians per second = rpm × (2π / 60). This works because one full revolution equals 2π radians, and there are 60 seconds in a minute. Multiplying rpm by this factor converts revolutions per minute into radians per second.
For example, converting 1 rpm: 1 × (2π / 60) = 2π / 60 ≈ 0.1047 rad/sec. This step-by-step method ensures accurate translation between units.
Conversion Example
- Convert 5 rpm:
- Multiply 5 by (2π / 60): 5 × 0.1047 ≈ 0.5236 rad/sec.
- This shows that 5 rpm equals about 0.5236 radians per second.
- Convert 10 rpm:
- 10 × 0.1047 ≈ 1.0472 rad/sec.
- So, 10 rpm converts to approximately 1.0472 radians per second.
- Convert 15 rpm:
- 15 × 0.1047 ≈ 1.5708 rad/sec.
- This means 15 rpm is about 1.5708 radians per second.
Conversion Chart
| rpm | rad/sec |
|---|---|
| -24.0 | -1.2570 |
| -23.0 | -1.2047 |
| -22.0 | -1.1524 |
| -21.0 | -1.1001 |
| -20.0 | -1.0472 |
| -19.0 | -0.9940 |
| -18.0 | -0.9411 |
| -17.0 | -0.8880 |
| -16.0 | -0.8351 |
| -15.0 | -0.7854 |
| -14.0 | -0.7322 |
| -13.0 | -0.6790 |
| -12.0 | -0.6283 |
| -11.0 | -0.5752 |
| -10.0 | -0.5236 |
| -9.0 | -0.4712 |
| -8.0 | -0.4189 |
| -7.0 | -0.3665 |
| -6.0 | -0.3142 |
| -5.0 | -0.2618 |
| -4.0 | -0.2094 |
| -3.0 | -0.1570 |
| -2.0 | -0.1047 |
| -1.0 | -0.0524 |
| 0.0 | 0.0 |
| 1.0 | 0.1047 |
| 2.0 | 0.2094 |
| 3.0 | 0.3142 |
| 4.0 | 0.4189 |
| 5.0 | 0.5236 |
| 6.0 | 0.6283 |
| 7.0 | 0.7330 |
| 8.0 | 0.8378 |
| 9.0 | 0.9425 |
| 10.0 | 1.0472 |
| 20.0 | 2.0944 |
| 30.0 | 3.1416 |
| 40.0 | 4.1888 |
| 50.0 | 5.2360 |
| 60.0 | 6.2832 |
| 70.0 | 7.3304 |
| 80.0 | 8.3776 |
| 90.0 | 9.4248 |
| 100.0 | 10.4720 |
| 120.0 | 12.5664 |
| 150.0 | 15.708 |
| 180.0 | 18.8496 |
| 200.0 | 20.9439 |
| 250.0 | 26.1799 |
Read the table from left to right, matching rpm values with rad/sec equivalents to find conversions quickly for any value in the range.
Related Conversion Questions
- How many radians per second is 1 rpm?
- What is the radian equivalent of 1 revolution per minute?
- Convert 1 rpm to radians per second for a motor speed?
- How do I change 1 rpm into radians for physics calculations?
- What is the rad/sec value when a wheel spins at 1 rpm?
- Can you show me the radian conversion for 1 rpm?
- How many radians does a 1 rpm rotation cover per second?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns an object makes each minute. It is a rotational speed unit used in motors, engines, and machinery, indicating how fast something spins around its axis.
rad
Radians are units of angular measurement where one radian equals the angle formed when the arc length equals the radius. It is a natural measure for angles in mathematics and physics, relating linear and rotational quantities.
Conversion FAQs
How do I convert 1 rpm to radians per second manually?
Multiply 1 rpm by (2π / 60). Since 1 rpm equals 2π radians divided by 60 seconds, the calculation yields approximately 0.1047 rad/sec. This method applies to any rpm value, just replace 1 with your number.
Why is the conversion factor 2π/60?
This factor comes from the fact that one revolution equals 2π radians, and there are 60 seconds in a minute. Multiplying rpm by this fraction converts revolutions per minute into radians per second, aligning the rotational units correctly.
Can I use this conversion to find rad/sec from any rpm value?
Yes, multiplying your rpm value by (2π / 60) gives the radians per second. This simple formula works across all rpm measurements, providing a consistent way to compare rotational speeds.
