Revolutions to Radians Converter
Quick answer: To convert revolutions to radians, multiply by 6.283185. For example, 10 rev is 62.83185 rad. One turn equals 6.283185 rad.
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Use the Revolutions to Radians Converter
Revolutions to Radians formula and what each symbol means
rad = rev × 6.283185
| Symbol | Meaning |
|---|---|
| rev | Turn |
| rad | Radian |
Revolutions to Radians examples
1 rev
1 rev × 6.283185 = 6.283185 rad.
10 rev
10 rev × 6.283185 = 62.83185 rad.
100 rev
100 rev × 6.283185 = 628.3185 rad.
Revolutions compared with Radians
One rev is 6.283 times as large as one rad, so your number gets bigger when you convert revolutions to radians and smaller when you convert back. If the answer is not larger than what you typed, you divided instead of multiplying.
About revolutions and radians
Turn (rev): One full turn, 360 degrees or 2π radians. Radian (rad): The SI unit of plane angle: the angle subtended by an arc equal to the radius.
Where revolutions to radians conversions are used
Navigation and surveying use degrees, while maths, physics and programming use radians. Machining and construction use degrees; some drafting and military work uses gradians or mils.
How to calculate Revolutions to Radians step by step
- Enter the value in rev (the starting unit).
- Multiply by 6.283185, because 1 rev = 6.283185 rad.
- The product is the value in rad. To go back, divide by 6.283185 or multiply by 0.1591549.
Popular angle conversions
How to read your Revolutions to Radians result
Quick estimate: multiply by about 6.3 to get radians from revolutions; this is within 0.3% of the exact factor. A full turn is 360 degrees, 400 gradians or 2π radians (about 6.28319).
| REVOLUTIONS | RADIANS |
|---|---|
| 1 | 6.283185 |
| 2 | 12.56637 |
| 5 | 31.41593 |
| 10 | 62.83185 |
| 20 | 125.6637 |
| 50 | 314.1593 |
| 100 | 628.3185 |
| 1,000 | 6,283.185 |
Radians to Revolutions: quick table
| RADIANS | REVOLUTIONS |
|---|---|
| 1 | 0.1591549 |
| 5 | 0.7957747 |
| 10 | 1.591549 |
| 25 | 3.978874 |
| 50 | 7.957747 |
| 100 | 15.91549 |
| 250 | 39.78874 |
| 500 | 79.57747 |
Common mistakes when calculating Revolutions to Radians
- Leaving a calculator in degree mode when the input is in radians (or the reverse).
- Dividing when you should multiply: from rev to rad multiply by 6.283185; from rad to rev divide by 6.283185.
Revolutions to Radians FAQ
How many rad are in 1 rev?
1 rev equals 6.283185 rad.
How many rev are in 1 rad?
1 rad equals 0.1591549 rev.
Is 1 rev = 6.283185 rad an exact conversion?
The factor is shown rounded to 7 significant figures (6.283185). The calculator above uses more digits.
What is a turn (rev)?
One full turn, 360 degrees or 2π radians.
How can I estimate revolutions to radians in my head?
Quick estimate: multiply by about 6.3 to get radians from revolutions; this is within 0.3% of the exact factor.
What is 3 rev in radians?
3 rev = 18.84956 rad (since 3 × 6.283185).
What is 30 rev in radians?
30 rev = 188.4956 rad (since 30 × 6.283185).
What is 150 rev in radians?
150 rev = 942.4778 rad (since 150 × 6.283185).
How many decimals should I keep when converting rev to rad?
Match the precision of your original measurement. For example, 62.83185 rad rounds to 62.8 rad at 3 significant figures; keep more digits only for engineering or scientific work.
More in Angle converters
- Degrees to Revolutions Converter
- Radians to Gradians Converter
- Gradians to Degrees Converter
- Radians to Degrees Converter
- Gradians to Radians Converter
- Gradians to Revolutions Converter
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Method, review and disclaimer
Edited by: Hemant Kumar and Anjita Rai, founders of ToolsVault (SEO and content professional, not a licensed adviser). Method: this tool runs in your browser using the formula shown on this page; the numbers you enter are not sent to our servers. Sources: NIST SP 811, Appendix B.8: conversion factors, BIPM: the SI derived units