5 RPM to Rad – Full Calculation Guide

The conversion of 5 rpm to radians results in approximately 0.5236 radians. This is because 1 rpm equals 2π/60 radians per second, so multiplying 5 by this conversion factor gives the value in rad.

To explain more, revolutions per minute (rpm) measure how many complete turns occur in one minute. Since one revolution equals 2π radians, converting rpm into radians involves multiplying the rpm value by 2π and then dividing by 60, because there are 60 seconds in a minute. For 5 rpm, the calculation is 5 × 2π / 60, which simplifies to 5 × π / 30, resulting in about 0.5236 radians.

Conversion Result

5 rpm is equal to approximately 0.5236 radians.

Conversion Tool

Enter value in rpm:

Result in rad:

Conversion Formula

The formula to convert rpm to radians per second is (rpm × 2π) / 60. This works because each revolution contains 2π radians, and rpm indicates how many such revolutions happen per minute. Dividing by 60 converts minutes to seconds, giving rad/sec.

For example, for 5 rpm: (5 × 2π) / 60 = (5 × 6.2832) / 60 = 31.416 / 60 ≈ 0.5236 radians/sec. The multiplication accounts for the radians per revolution, and the division adjusts for time in seconds.

Conversion Example

• Convert 10 rpm:
  • Multiply 10 by 2π: 10 × 6.2832 = 62.832
  • Divide by 60: 62.832 / 60 = 1.0472 rad
• Convert 15 rpm:
  • 15 × 6.2832 = 94.248
  • 94.248 / 60 = 1.5708 rad
• Convert 20 rpm:
  • 20 × 6.2832 = 125.664
  • 125.664 / 60 = 2.0944 rad
• Convert 25 rpm:
  • 25 × 6.2832 = 157.08
  • 157.08 / 60 = 2.618 rad
• Convert 30 rpm:
  • 30 × 6.2832 = 188.496
  • 188.496 / 60 = 3.1416 rad

Conversion Chart

rpm	rad
-20.0	-2.0944
-15.0	-1.5708
-10.0	-1.0472
-5.0	-0.5236
0.0	0.0
5.0	0.5236
10.0	1.0472
15.0	1.5708
20.0	2.0944
25.0	2.6180
30.0	3.1416

The chart shows values from -20 to 30 rpm and their radian equivalents. Use it to quickly approximate conversion results for different rpm values by matching the rpm to the corresponding radian measure.

Related Conversion Questions

• How many radians are in 5 rpm?
• What is the radian equivalent of 5 rpm?
• Convert 5 rpm to radians per second?
• How do I calculate radians from rpm for 5 revolutions per minute?
• What is the radian measure for 5 rpm in a rotating system?
• Can I convert 5 rpm to radians using an online calculator?
• What is the formula to change rpm into radians per second for 5 rpm?

Conversion Definitions

rpm

Revolutions per minute (rpm) measures how many complete turns or cycles an object makes in one minute, used in engines, motors, and rotating machinery to indicate speed or rotational rate.

rad

Radian (rad) is a unit of angular measurement representing the angle created when the arc length equals the radius of a circle, with 2π radians equaling one full revolution around the circle.

Conversion FAQs

How does changing rpm affect the radians per second?

Increasing rpm increases the radians per second proportionally, as more revolutions per minute translate directly into a higher angular velocity in radians/sec, based on the conversion formula.

Why is 2π used in the conversion from rpm to radians?

Because 2π radians correspond to one full revolution, multiplying rpm by 2π converts revolutions into radians, allowing the calculation of angular displacement in rad/sec.

Can I convert any rpm value to radians per second with this method?

Yes, as long as you apply the formula (rpm × 2π) / 60, you can convert any rpm to radians per second accurately, regardless of the magnitude of the rpm value.

What does the division by 60 represent in the formula?

The division by 60 converts the rate from per minute to per second, because there are 60 seconds in a minute, ensuring the angular velocity is expressed in radians/sec.

Is there a direct way to convert rpm to radians without using the formula?

While a direct mental conversion is possible by multiplying rpm by π/30, using the formula ensures accuracy and is the most straightforward method for consistent results.