60 rpm is approximately 6.2832 radians per second.
This conversion means that rotating at 60 revolutions per minute (rpm) corresponds to about 6.2832 radians each second because one revolution equals 2π radians, and there are 60 seconds in a minute, so we convert rpm to radians per second using this relationship.
Conversion Result
60 rpm equals 6.2832 rad.
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 each revolution contains 2π radians, and there are 60 seconds in a minute. By multiplying rpm with 2π, you get radians per minute, and dividing by 60 converts to seconds.
For example, converting 60 rpm: 60 * (2π) / 60 = 2π ≈ 6.2832 rad/sec. This calculation confirms that 60 rpm equals approximately 6.2832 radians per second.
Conversion Example
- Convert 30 rpm:
- Multiply 30 by 2π: 30 * 6.2832 = 188.496
- Divide 188.496 by 60: 188.496 / 60 = 3.1416 rad/sec
- Result: 30 rpm is approximately 3.1416 rad/sec.
- Convert 90 rpm:
- Multiply 90 by 2π: 90 * 6.2832 = 565.488
- Divide 565.488 by 60: 565.488 / 60 = 9.4248 rad/sec
- Result: 90 rpm is about 9.4248 rad/sec.
- Convert 15 rpm:
- Multiply 15 by 2π: 15 * 6.2832 = 94.248
- Divide 94.248 by 60: 94.248 / 60 = 1.5708 rad/sec
- Result: 15 rpm is approximately 1.5708 rad/sec.
- Convert 120 rpm:
- Multiply 120 by 2π: 120 * 6.2832 = 753.984
- Divide 753.984 by 60: 753.984 / 60 = 12.5664 rad/sec
- Result: 120 rpm equals around 12.5664 rad/sec.
Conversion Chart
| rpm | rad/sec |
|---|---|
| 35.0 | 3.6652 |
| 40.0 | 4.1888 |
| 45.0 | 4.7124 |
| 50.0 | 5.2360 |
| 55.0 | 5.7596 |
| 60.0 | 6.2832 |
| 65.0 | 6.8068 |
| 70.0 | 7.3304 |
| 75.0 | 7.8540 |
| 80.0 | 8.3776 |
| 85.0 | 8.9012 |
Use this chart to quickly see how various rpm values convert to radians per second, helpful for quick reference during calculations or design work.
Related Conversion Questions
- How many radians per second are in 60 rpm?
- What is the rad/sec value for 60 revolutions per minute?
- Convert 60 rpm to radians per second, what do I get?
- How do I change 60 rpm into radians per second?
- What’s the radian measure equivalent of 60 rpm?
- Is 60 rpm equal to about 6.2832 radians per second?
- How to calculate radians per second from 60 rpm?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns an object makes each minute, used in machinery and engines to indicate rotational speed.
rad
Radians (rad) are a way to measure angles based on the radius of a circle, with one full revolution equaling 2π radians, widely used in mathematics and physics to quantify rotational quantities.
Conversion FAQs
Why do we multiply rpm by 2π and divide by 60 in the conversion?
This operation converts revolutions per minute into radians per second because each revolution contains 2π radians, and dividing by 60 accounts for seconds in a minute, giving the rotation rate in radians per second.
Can I convert rpm to rad/sec with a simple calculator?
Yes, by using the formula radians/sec = rpm * (2π) / 60, you can easily perform the conversion with any calculator, making sure to include π accurately or use a calculator that has π built-in.
What is the significance of radians in rotational measurements?
Radians provide a natural way to measure angles based on the circle’s radius, simplifying calculations involving rotational motion, as many formulas in physics and engineering are expressed more cleanly using radians instead of degrees.
Are there other units to measure rotational speed?
Yes, besides rpm and radians per second, rotational speed can also be expressed in degrees per second, revolutions per hour, or cycles per minute, but radians/sec and rpm are most common in technical contexts.