300 rpm equals approximately 31.4168 radians per second.
To convert revolutions per minute (rpm) to radians per second (rad/s), multiply rpm by 2π and divide by 60. This is because one revolution equals 2π radians, and there are 60 seconds in a minute, so the calculation adjusts for time unit differences and converts revolutions to radians.
Conversion Result
The calculation for 300 rpm to rad is: (300 × 2π) / 60 = (300 × 6.2832) / 60 ≈ 31.4168 rad/sec.
Conversion Tool
Result in rad:
Conversion Formula
To convert rpm to rad, the formula is (rpm × 2π) / 60. This works because each revolution is 2π radians, and dividing by 60 converts minutes into seconds. The multiplication brings revolutions into radians, and dividing adjusts for time units used.
For example, with 300 rpm: 300 × 2π = 600π radians per minute, then dividing by 60 gives 10π radians per second, which equals approximately 31.4168 rad/sec.
Conversion Example
- Convert 150 rpm:
- Multiply 150 by 2π: 150 × 6.2832 = 942.48 radians per minute.
- Divide by 60: 942.48 / 60 ≈ 15.708 rad/sec.
- Convert 450 rpm:
- 450 × 2π = 2827.43 radians per minute.
- Divide by 60: 2827.43 / 60 ≈ 47.124 rad/sec.
- Convert 600 rpm:
- 600 × 2π = 3769.91 radians per minute.
- Divide by 60: 3769.91 / 60 ≈ 62.832 rad/sec.
- Convert 90 rpm:
- 90 × 2π = 565.49 radians per minute.
- Divide by 60: 565.49 / 60 ≈ 9.425 rad/sec.
- Convert 120 rpm:
- 120 × 2π = 753.98 radians per minute.
- Divide by 60: 753.98 / 60 ≈ 12.566 rad/sec.
Conversion Chart
| rpm | rad/sec |
|---|---|
| 275.0 | 28.7690 |
| 280.0 | 29.3215 |
| 285.0 | 29.8740 |
| 290.0 | 30.4265 |
| 295.0 | 30.9790 |
| 300.0 | 31.5315 |
| 305.0 | 32.0840 |
| 310.0 | 32.6365 |
| 315.0 | 33.1890 |
| 320.0 | 33.7415 |
| 325.0 | 34.2940 |
The table shows rpm values from 275 to 325 and their equivalent rad/sec. To read it, locate the rpm value and see the corresponding rad/sec. Use this chart to quickly estimate conversions for values within this range.
Related Conversion Questions
- What is the rad/sec equivalent of 300 rpm?
- How do I convert 300 revolutions per minute into radians per second?
- What is 300 rpm in terms of angular velocity in radians?
- If a motor spins at 300 rpm, what is its rotation speed in radians per second?
- Can you tell me how 300 rpm relates to radians per second?
- What is the radian measure for 300 rpm rotation speed?
- How do I calculate radians per second from 300 rpm?
Conversion Definitions
rpm
Revolutions per minute (rpm) is a measurement of rotational speed indicating how many complete turns or revolutions an object makes in one minute, often used in motors and machinery to describe spinning velocities.
rad
Radian (rad) is a unit of angular measurement that represents the angle subtended by an arc equal in length to the radius of a circle, with 2π radians equaling one complete revolution.
Conversion FAQs
How accurate is the conversion from rpm to rad/sec?
The conversion is precise when using the exact value of π (pi). The standard formula (rpm × 2π) / 60 provides a reliable result, but rounding π can introduce minor errors, which are negligible for most practical applications.
Can I convert rad/sec back to rpm using the same formula?
Yes, reversing the process involves multiplying rad/sec by 60 and dividing by 2π: rpm = (rad/sec × 60) / 2π. This allows you to switch between units easily depending on your measurement needs.
Why is 60 used in the formula?
The number 60 converts minutes into seconds because rpm measures revolutions per minute, but radians per second are based on seconds. This factor ensures unit consistency and accurate conversion.
What happens if I input a negative rpm value?
A negative rpm indicates rotation in the opposite direction. The conversion formula remains the same; only the sign changes, reflecting the direction of rotation rather than the magnitude of angular velocity.