Converting 60 rpm to radians gives approximately 6.2832 radians. This shows that rotating at 60 revolutions per minute equals about 6.2832 radians per second.
To convert rpm to radians per second, you multiply the revolutions per minute by 2π and then divide by 60, because there are 2π radians in one revolution and 60 seconds in a minute. So, 60 rpm times 2π divided by 60 equals 2π radians, which is approximately 6.2832 radians.
Conversion Result
60 rpm equals approximately 6.2832 radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to radians per second 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, then dividing by 60 converts it to radians per second. For example, 60 rpm: (60 * 2π) / 60 = 2π = approximately 6.2832 rad/sec.
Conversion Example
- Convert 120 rpm to radians per second:
- Use formula: (120 * 2π) / 60
- Calculate numerator: 120 * 6.2832 = 753.98
- Divide by 60: 753.98 / 60 = 12.566 radians/sec
- Result: approximately 12.566 rad/sec
- Convert 30 rpm to radians per second:
- Apply formula: (30 * 2π) / 60
- Calculate numerator: 30 * 6.2832 = 188.50
- Divide by 60: 188.50 / 60 = 3.1416 radians/sec
- Result: approximately 3.1416 rad/sec
- Convert 90 rpm to radians per second:
- Use formula: (90 * 2π) / 60
- Calculate numerator: 90 * 6.2832 = 565.49
- Divide by 60: 565.49 / 60 = 9.4248 radians/sec
- Result: approximately 9.4248 rad/sec
Conversion Chart
| rpm | radians/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 rpm values convert to radians per second. Find the rpm value in the first column, then look at the corresponding rad/sec in the second column.
Related Conversion Questions
- How many radians per second are in 60 rpm?
- What is the rad/sec equivalent of 60 rpm?
- How do I convert 60 rpm to radians per second manually?
- What’s the rad/sec value for 60 rpm in a motor?
- Can I use a calculator to convert 60 rpm to rad/sec?
- What is the formula to change rpm into radians per second?
- How fast is 60 rpm in radians per second?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns an object makes each minute, indicating rotational speed. It is used in engines, motors, and machinery to describe how fast something spins.
rad
Radians (rad) are a unit of angular measure representing the angle created by wrapping an arc length equal to the radius around a circle. One radian equals about 57.2958 degrees, and it describes the size of an angle in radians.
Conversion FAQs
How do I convert 60 rpm into radians per second manually?
To convert 60 rpm into radians per second, multiply 60 by 2π and then divide by 60. This simplifies to 2π radians per second, which is approximately 6.2832 rad/sec. So, 60 rpm equals about 6.2832 radians/sec.
Why is the conversion factor 2π/60?
This factor arises because one revolution contains 2π radians, and there are 60 seconds in a minute. Multiplying rpm by 2π gives radians per minute, and dividing by 60 converts it to radians per second, providing the standard conversion.
Can I convert any rpm value to radians per second using this formula?
Yes, this formula works for any rpm value. Just multiply the rpm by 2π and divide by 60 to find radians per second, making it a universal way to convert rotational speed units.
What is the significance of radians in rotational speed?
Radians provide a natural measure of angles in mathematics, and in rotational speed, they relate directly to the arc length and the angle of rotation. Using radians simplifies calculations in physics and engineering involving rotational motion.
Last Updated : 30 May, 2025
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Sandeep Bhandari holds a Bachelor of Engineering in Computers from Thapar University (2006). He has 20 years of experience in the technology field. He has a keen interest in various technical fields, including database systems, computer networks, and programming. You can read more about him on his bio page.