15 rpm equals approximately 1.57 radians per second. When converting 15 rpm to rad, we find that it’s about 1.57 rad/sec.

To convert revolutions per minute to radians per second, we need to understand that one revolution equals 2π radians, and one minute equals 60 seconds. So, multiplying rpm by 2π and then dividing by 60 gives us radians per second.

Calculation of 15 rpm to rad

Given 15 rpm, the conversion formula is: radians per second = rpm × (2π radians) / 60 seconds. Plug in 15: radians/sec = 15 × (2π) / 60. Simplify: (15 / 60) × 2π = 0.25 × 2π = 0.5π ≈ 1.57 rad/sec.

Conversion Tool

Conversion Formula

The formula to convert rpm to radians per second is radians/sec = rpm × (2π) / 60. This formula works because a revolution contains 2π radians, and there are 60 seconds in a minute. Multiplying rpm by 2π gives radians per minute, dividing by 60 yields radians per second. For example, at 15 rpm: 15 × 2π / 60 = 0.5 × 2π = 1.57 rad/sec.

Conversion Example

• Convert 20 rpm:
  • Use formula: 20 × 2π / 60
  • Calculate numerator: 20 × 6.2832 ≈ 125.664
  • Divide by 60: 125.664 / 60 ≈ 2.094 rad/sec
• Convert 5 rpm:
  • Use formula: 5 × 2π / 60
  • Calculate numerator: 5 × 6.2832 ≈ 31.416
  • Divide by 60: 31.416 / 60 ≈ 0.524 rad/sec
• Convert 30 rpm:
  • Use formula: 30 × 2π / 60
  • Calculate numerator: 30 × 6.2832 ≈ 188.496
  • Divide by 60: 188.496 / 60 ≈ 3.141 rad/sec
• Convert 10 rpm:
  • Use formula: 10 × 2π / 60
  • Calculate numerator: 10 × 6.2832 ≈ 62.832
  • Divide by 60: 62.832 / 60 ≈ 1.047 rad/sec

Conversion Chart

Use this chart to quickly find the radian values for the rpm values listed. Just find the rpm on the left column and look across to see the corresponding radians per second.

Related Conversion Questions

• How many radians per second is 15 rpm?
• What is the rad/sec equivalent of 15 rpm?
• Convert 15 revolutions per minute to radians per second?
• How do I turn 15 rpm into radians per second manually?
• What is the radian measure of 15 rpm?
• Is 15 rpm equal to approximately 1.57 radians per second?
• How can I convert rpm to radians per second for any value?

Conversion Definitions

rpm: Revolutions per minute, a measure of rotational speed indicating how many complete turns are made in one minute. It’s used in engines, motors, and machinery to describe how fast something spins.

rad: Radians, a unit measuring angles based on the radius of a circle. One radian is the angle where the arc length equals the radius. Radians are often used in mathematics and physics to express rotational quantities.

Conversion FAQs

Why is 15 rpm equal to about 1.57 radians per second?

This is because converting rpm to rad/sec involves multiplying by 2π and dividing by 60. For 15 rpm, the calculation results in approximately 1.57 radians per second, which represents how fast the object rotates in radians each second.

Can I use the same formula to convert other rpm values to radians per second?

Yes, the formula radians/sec = rpm × (2π) / 60 works for any rpm value. Just replace rpm with the number you want to convert, and the calculation will give you the radians per second.

What does one revolution correspond to in radians?

One revolution is 2π radians, because the circle’s circumference in radians is 2π times the radius. This conversion basis is used to turn revolutions into radians for calculations involving angular measurement.

Is there an easier way to estimate radians per second without a calculator?

For quick estimates, note that 1 rpm roughly equals 0.105 radians per second. So, for 15 rpm, multiply 15 by 0.105 to get approximately 1.58 radians per second. But for precise results, use the full formula.