20 rpm equals approximately 2.0944 radians per second.
This conversion is based on the fact that revolutions per minute (rpm) can be converted to radians per second (rad/s) by multiplying by a factor of 2π/60. Since one revolution equals 2π radians, dividing by 60 converts minutes to seconds.
Conversion Result and Explanation
Converting 20 rpm to radians involves multiplying the rpm value by the factor 2π divided by 60. This transforms revolutions per minute into radians per second, providing a standard measure of rotational speed in the radian unit per second.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm (revolutions per minute) to rad/s (radians per second) is: rpm × (2π / 60). It works because each revolution is equal to 2π radians, and dividing by 60 converts minutes into seconds. For example, 20 rpm times 2π/60 gives the rad/s value.
Step-by-step math: 20 rpm × (2π / 60) = 20 × (6.2832 / 60) = 20 × 0.10472 = 2.0944 rad/s.
Conversion Example
- Convert 10 rpm:
- Apply formula: 10 × 2π/60.
- Calculate: 10 × 0.10472.
- Result: 1.0472 rad/s.
- Convert 50 rpm:
- Apply formula: 50 × 2π/60.
- Calculate: 50 × 0.10472.
- Result: 5.2360 rad/s.
- Convert 100 rpm:
- Apply formula: 100 × 2π/60.
- Calculate: 100 × 0.10472.
- Result: 10.472 rad/s.
Conversion Chart
| rpm | rad/s |
|---|---|
| -5.0 | -0.5236 |
| 0.0 | 0.0000 |
| 5.0 | 0.5236 |
| 10.0 | 1.0472 |
| 15.0 | 1.5708 |
| 20.0 | 2.0944 |
| 25.0 | 2.6180 |
| 30.0 | 3.1416 |
| 35.0 | 3.6652 |
| 40.0 | 4.1888 |
| 45.0 | 4.7124 |
This chart helps you quickly see the radian per second equivalent for rpm values from -5 to 45. Use it to find approximate conversions without calculations.
Related Conversion Questions
- How many radians per second are in 20 rpm?
- What is the radian equivalent of 20 revolutions per minute?
- Convert 20 rpm into radians per second without a calculator.
- What is the rad/s value for 20 rpm in a rotation speed measurement?
- How do I change 20 rpm to radians per second?
- Is 20 rpm equal to approximately 2 radians per second?
- Can I convert 20 rpm to radians per second using a simple formula?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute, indicating rotational speed. It’s a common unit in engines, turbines, and rotating machinery, showing how fast something spins.
rad
Rad, short for radian, is a unit of angular measure that describes the angle created when the arc length equals the radius of a circle. One radian is approximately 57.2958 degrees, and it is used in calculations involving angles and circular motion.
Conversion FAQs
How accurate is the conversion from rpm to rad/s?
The conversion is highly accurate because it relies on the exact mathematical relationship between revolutions and radians, and the precise value of π. Minor differences may occur due to rounding in intermediate steps or display.
Can I convert rad/s back to rpm using the same formula?
Yes, reversing the process involves multiplying rad/s by 60 and dividing by 2π. The formula: rpm = rad/s × (60 / 2π). This allows you to switch between these units as needed.
Why do we use radians instead of degrees in these conversions?
Radians are mathematically more natural for calculations involving calculus, trigonometry, and physics because they relate directly to the properties of circles. Degrees are more common for practical or visual measurements but less suited for formulas.
I’ve put so much effort writing this blog post to provide value to you. It’ll be very helpful for me, if you consider sharing it on social media or with your friends/family. SHARING IS ♥️
