400 rpm is approximately 41.89 radians per second.
This conversion is done by recognizing that revolutions per minute (rpm) to radians per second involves multiplying the rpm value by 2π (since one revolution is 2π radians) and then dividing by 60 (seconds in a minute). So, 400 rpm equals (400 × 2π) / 60 ≈ 41.89 rad/sec.
Conversion of 400 rpm to radians
To convert 400 rpm to radians per second, first understand that one revolution equals 2π radians. Since rpm measures how many revolutions occur every minute, you multiply rpm by 2π to get radians per minute. Then, divide by 60 to convert to radians per second. This process ensures a precise conversion between these units of rotational speed.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert rpm to rad/sec is: radians per second = (rpm × 2π) / 60. This works because each revolution is 2π radians, and there are 60 seconds in a minute. Multiplying rpm by 2π gives radians per minute, dividing by 60 converts it to radians per second. For example, 400 rpm times 2π yields 2513.27 radians per minute, then dividing by 60 results in approximately 41.89 rad/sec.
Conversion Example
- Convert 600 rpm to rad/sec:
- Multiply 600 by 2π: 600 × 6.2832 ≈ 3769.91 radians per minute.
- Divide by 60: 3769.91 / 60 ≈ 62.83 rad/sec.
- So, 600 rpm equals approximately 62.83 radians per second.
- Convert 250 rpm to rad/sec:
- Multiply 250 by 2π: 250 × 6.2832 ≈ 1570.80 radians per minute.
- Divide by 60: 1570.80 / 60 ≈ 26.18 rad/sec.
- Thus, 250 rpm is about 26.18 radians per second.
- Convert 100 rpm to rad/sec:
- Multiply 100 by 2π: 100 × 6.2832 ≈ 628.32 radians per minute.
- Divide by 60: 628.32 / 60 ≈ 10.47 rad/sec.
- Therefore, 100 rpm is approximately 10.47 radians per second.
- Convert 50 rpm to rad/sec:
- Multiply 50 by 2π: 50 × 6.2832 ≈ 314.16 radians per minute.
- Divide by 60: 314.16 / 60 ≈ 5.24 rad/sec.
- So, 50 rpm equals roughly 5.24 radians per second.
Conversion Chart
| rpm | Radians per second (rad/sec) |
|---|---|
| 375.0 | 39.27 |
| 380.0 | 39.80 |
| 385.0 | 40.33 |
| 390.0 | 40.86 |
| 395.0 | 41.39 |
| 400.0 | 41.89 |
| 405.0 | 42.42 |
| 410.0 | 42.95 |
| 415.0 | 43.48 |
| 420.0 | 44.01 |
| 425.0 | 44.54 |
This chart shows how different rpm values convert into rad/sec, making it easier to estimate the rotational speed in radians for specific rpm numbers without recalculating each time.
Related Conversion Questions
- How many radians per second is 400 rpm in rotational speed?
- What is the rad/sec equivalent of 400 rpm?
- Can you convert 400 revolutions per minute to radians per second?
- What is the rad/sec value for 400 rpm?
- How do I change 400 rpm into radians for physics calculations?
- What is the conversion from 400 rpm to angular velocity in radians?
- How many radians per second are in 400 rpm of a motor?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns an object makes in one minute. It helps quantify rotational speed, especially in engines and rotating machinery, by counting complete revolutions within a set time frame.
rad
Radians (rad) are units of angular measure, representing the angle subtended by an arc equal in length to the radius. One full revolution equals 2π radians, and it’s used in mathematics and physics to describe rotational positions and speeds.
Conversion FAQs
What is the significance of converting rpm to radians?
Converting rpm to radians provides a more precise measure of angular velocity, essential in physics and engineering where calculations involve torque, angular acceleration, or rotational energy. Radians are a natural unit in formulas involving angular motion.
How accurate is the conversion from rpm to radians per second?
The conversion is highly accurate because it relies on the exact relationship between revolutions and radians (2π radians per revolution). Using the formula (rpm × 2π)/60 ensures precise results for any rpm value.
Why do engineers prefer radians over rpm?
Engineers prefer radians because they simplify mathematical equations involving rotational motion, such as calculating angular acceleration, torque, and kinetic energy. Radians are directly related to the geometry of circles, making calculations more straightforward.
Can I convert any rpm value to radians per second using this method?
Yes, the method applies universally for any rpm value. Just multiply the rpm by 2π and divide by 60 to get radians per second, regardless of the magnitude of the rpm number.
Last Updated : 31 May, 2025
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Sandeep Bhandari holds a Bachelor of Engineering in Computers from Thapar University (2006). He has 20 years of experience in the technology field. He has a keen interest in various technical fields, including database systems, computer networks, and programming. You can read more about him on his bio page.