200 RPM to Rad – Easy Conversion Explained

The result of converting 200 rpm to radians per second is approximately 20.9439 rad/sec.

To convert revolutions per minute (rpm) into radians per second, you multiply the rpm value by 2π (since one revolution equals 2π radians) and then divide by 60 seconds (since there are 60 seconds in a minute). This process transforms the rotational speed into an angular velocity expressed in radians per second.

Conversion Result

Conversion Formula

The formula to change rpm to rad/sec is: radians per second = (rpm × 2π) / 60. This works because each revolution is 2π radians, and dividing by 60 converts revolutions per minute into revolutions per second. Multiplying rpm by 2π gives the radians per minute, then dividing by 60 gives radians per second.

For example, if rpm is 200, then radians per second = (200 × 2π) / 60 = (200 × 6.2832) / 60 = 1256.64 / 60 ≈ 20.9439 rad/sec.

Conversion Example

• Convert 100 rpm:
  • Multiply 100 by 2π: 100 × 6.2832 = 628.32 radians per minute.
  • Divide by 60 seconds: 628.32 / 60 ≈ 10.472 rad/sec.
• Convert 50 rpm:
  • 50 × 2π = 314.16 radians per minute.
  • 314.16 / 60 ≈ 5.236 rad/sec.
• Convert 300 rpm:
  • 300 × 2π = 1884.96 radians per minute.
  • 1884.96 / 60 ≈ 31.416 rad/sec.
• Convert 250 rpm:
  • 250 × 2π = 1570.80 radians per minute.
  • 1570.80 / 60 ≈ 26.180 rad/sec.
• Convert 75 rpm:
  • 75 × 2π = 471.24 radians per minute.
  • 471.24 / 60 ≈ 7.854 rad/sec.

Conversion Chart

This chart shows how various rpm values translate into radians per second, from 175.0 to 225.0 in steps of 10:

To read this chart, find your rpm value on the left column, then look across to see the corresponding rad/sec on the right. This helps quickly estimate angular velocities without calculations.

Related Conversion Questions

• What is 200 rpm in radians per second?
• How do I convert 200 rpm to radians per second manually?
• What is the rad/sec equivalent of 200 revolutions per minute?
• How many radians per second is 200 rpm?
• Can I easily convert 200 rpm to radians per second online?
• What is the angular velocity in radians/sec for 200 rpm?
• How do I change 200 rpm into radians per second for a motor?

Conversion Definitions

rpm

Revolutions per minute (rpm) measures how many complete turns an object makes in one minute. It indicates rotational speed, used in machinery and engines, and is calculated by counting revolutions over 60 seconds.

rad

Radian (rad) is a unit of angular measurement representing the angle formed when the arc length equals the radius of a circle. One radian is about 57.2958 degrees, used in mathematics and physics to describe angles and rotational quantities.

Conversion FAQs

How do I convert rpm to radians per second for different values?

To convert rpm to radians per second, multiply the rpm value by 2π and then divide by 60 seconds. For each specific rpm, just follow this formula: radians/sec = (rpm × 2π) / 60. This process works for any rpm value, giving a consistent measure of angular velocity.

Why is 2π used in the conversion formula?

Because one full revolution is equivalent to 2π radians, multiplying rpm by 2π converts revolutions into radians, which are a more precise measure of rotation, especially for calculations involving angular velocity and physics applications.

What are some common applications where converting rpm to radians/sec is useful?

This conversion is essential in engineering, motor control, physics, and robotics, where understanding the angular velocity in radians/sec helps in designing systems, analyzing rotational motion, and synchronizing components accurately.

Is there an easy way to do this conversion without calculations?

Yes, using online calculators, conversion tools, or embedded formulas in software like spreadsheets. Enter the rpm value, and these tools will perform the calculation instantly, saving time and reducing errors in manual math.

What happens if I input a negative rpm value?

A negative rpm indicates rotation in the opposite direction. The conversion to radians/sec will also be negative, reflecting the direction of rotation, which is useful in systems where direction matters, such as in motor controls or physics simulations.