15 RPM to Rad – Full Calculation Guide

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15 rpm equals approximately 1.57 radians.

To convert 15 revolutions per minute (rpm) into radians, multiply by 2π and divide by 60 seconds. This is because one revolution is 2π radians, and there are 60 seconds in a minute, so the conversion accounts for both the angle in radians and the time units.

Conversion Result

15 rpm = 1.57 rad

Conversion Tool

Conversion Formula

The formula to convert rpm to radians per second is: radians = rpm × 2π / 60. This works because each revolution is 2π radians, and dividing by 60 converts minutes to seconds. Multiplying rpm by 2π gives radians per minute, then dividing by 60 gives radians per second.

For example, with 15 rpm: 15 × 2π / 60 = (15 × 6.2832) / 60 ≈ 94.248 / 60 ≈ 1.57 radians per second.

Conversion Example

• Convert 20 rpm to rad:
  • Step 1: Use formula: 20 × 2π / 60
  • Step 2: Calculate 2π ≈ 6.2832
  • Step 3: Multiply 20 by 6.2832 = 125.664
  • Step 4: Divide by 60 = 2.0944 rad
• Convert 5 rpm to rad:
  • Step 1: 5 × 2π / 60
  • Step 2: 5 × 6.2832 = 31.416
  • Step 3: Divide 31.416 by 60 = 0.5236 rad
• Convert 30 rpm to rad:
  • Step 1: 30 × 2π / 60
  • Step 2: 30 × 6.2832 = 188.496
  • Step 3: Divide 188.496 by 60 ≈ 3.1416 rad
• Convert 10 rpm to rad:
  • Step 1: 10 × 2π / 60
  • Step 2: 10 × 6.2832 = 62.832
  • Step 3: Divide 62.832 by 60 ≈ 1.0472 rad
• Convert 25 rpm to rad:
  • Step 1: 25 × 2π / 60
  • Step 2: 25 × 6.2832 = 157.08
  • Step 3: Divide 157.08 by 60 ≈ 2.618 rad

Conversion Chart

The table below shows rpm values from -10.0 to 40.0 and their equivalent in radians per second. Use this chart to quickly find conversions for common rpm values without calculation.

Related Conversion Questions

• What is the radian equivalent of 15 rpm?
• How do I convert 15 revolutions per minute into radians?
• What formula do I use to change rpm to radians per second?
• Can I quickly estimate radians for 15 rpm without calculator?
• How many radians per second in 15 rpm?
• What is the angular velocity in radians if a motor spins at 15 rpm?
• How to convert revolutions per minute to radians per second for a rotating shaft?

Conversion Definitions

rpm: Revolutions per minute measures how many complete turns an object makes in one minute, used to describe rotational speed in machinery and engines, representing the number of full rotations completed each minute.

rad: Radians are units of angular measure; one radian equals the angle at the center of a circle subtended by an arc equal in length to the circle’s radius, used to quantify rotation and angular displacement.

Conversion FAQs

How do I convert 15 rpm to radians per second manually?

Multiply the rpm value by 2π and then divide by 60. For 15 rpm: 15 × 2π / 60 = (15 × 6.2832) / 60 ≈ 1.57 rad/sec. This accounts for the angle in radians and converts minutes to seconds.

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

Because one full revolution corresponds to 2π radians. Multiplying rpm by 2π converts revolutions per minute into radians per minute, which is necessary for angular measurements in radians.

Can the conversion be done with a calculator or only by hand?

This conversion can be easily done with a calculator by plugging in the formula: rpm × 2π / 60. Using a calculator makes it faster and less prone to errors, especially for multiple values.

Is the conversion the same for all rotational speeds?

Yes, the formula applies universally. No matter the rpm value, multiplying by 2π and dividing by 60 converts rpm into radians per second, regardless of how fast or slow the rotation is.

What is the significance of radians in rotational calculations?

Radians provide a natural measure of angles based on the radius of a circle, making calculations involving rotational motion, angular velocity, and acceleration more straightforward and mathematically consistent.