Angle Converter
Quick answer: Choose a starting unit and a target unit, then enter a value. Common conversions: 1 ° = 0.01745329 rad; 1 ° = 1.111111 grad; 1 ° = 0.002777778 rev. This converter covers 7 angle units.
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Use the Angle Converter
Angle formula and what each symbol means
target = value × (factor of starting unit ÷ factor of target unit), where each factor is the unit value in °.
| Symbol | Meaning |
|---|---|
| value | The number you want to convert |
| factor | The unit’s size expressed in the base unit (°) |
Angle examples
° to rad
10 ° = 0.1745329 rad.
° to grad
10 ° = 11.11111 grad.
° to rev
10 ° = 0.02777778 rev.
How to calculate Angle step by step
- Choose the starting unit and the target unit.
- Enter your value.
- Read the converted value, plus the conversion factor in both directions.
Popular angle conversions
- Degrees to Radians converter
- Degrees to Gradians converter
- Degrees to Revolutions converter
- Radians to Degrees converter
- Radians to Gradians converter
- Radians to Revolutions converter
- Gradians to Degrees converter
- Gradians to Radians converter
- Gradians to Revolutions converter
- Revolutions to Degrees converter
- Revolutions to Radians converter
- Revolutions to Gradians converter
How to read your Angle result
A full turn is 360 degrees, 400 gradians or 2π radians (about 6.28319). To convert degrees to radians multiply by π/180, and to convert radians to degrees multiply by 180/π.
| UNIT | SYMBOL | EQUALS | VALUE OF 1 ° |
|---|---|---|---|
| Degree | ° | 1 ° = 1 ° | 1 ° |
| Radian | rad | 1 rad = 57.29578 ° | 0.01745329 rad |
| Gradian | grad | 1 grad = 0.9 ° | 1.111111 grad |
| Arcminute | ′ | 1 ′ = 0.016666667 ° | 60 ′ |
| Arcsecond | ″ | 1 ″ = 0.00027777778 ° | 3,600 ″ |
| Turn (revolution) | rev | 1 rev = 360 ° | 0.002777778 rev |
| Milliradian | mrad | 1 mrad = 0.05729578 ° | 17.45329 mrad |
Common mistakes when calculating Angle
- Leaving a calculator in degree mode when the input is in radians (or the reverse).
- Using 3.14 for π when high accuracy is needed.
- Mixing gradians (400 per turn) with degrees (360 per turn).
Angle FAQ
How many degrees are in a radian?
One radian is about 57.2958 degrees.
How many radians are in a degree?
One degree is π/180, about 0.0174533 radians.
How many gradians are in a right angle?
A right angle is 100 gradians.
What is the base unit for angle?
This converter uses degree (°) as the common base unit: every value is first converted to it and then to the target unit.
How do I convert between two angle units?
Choose the starting and target units, enter the value and read the result. By hand: convert to the base unit with the table, then divide by the target unit factor.
How many radians are in 1 degree?
1 ° = 0.01745329 rad.
How many gradians are in 1 degree?
1 ° = 1.111111 grad.
How many revolutions are in 1 degree?
1 ° = 0.002777778 rev.
Which angle units does this converter support?
It covers 7 units: degree (°), radian (rad), gradian (grad), arcminute (′), arcsecond (″), turn (rev), milliradian (mrad).
How accurate is the angle converter?
Results are calculated at full double precision and shown to about 8 significant figures. Round the answer to the precision of your original measurement; a result cannot be more accurate than the number you started with.
More in Angle converters
- Revolutions to Radians Converter
- Revolutions to Gradians Converter
- Revolutions to Degrees Converter
- Gradians to Degrees Converter
- Radians to Revolutions Converter
- Gradians to Radians 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