Angle Converter
General
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Formula
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What this converter does
This converter turns degrees into radians and back instantly. It also covers gradians, arcminutes, arcseconds and turns — every pair uses an exact factor. Type a value, pick your units, and read the result as you type.
Half a turn is 180° = π radians, so degrees × π/180 gives radians. Unit definitions follow NIST.
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The units it covers
Every angle unit converts through the degree with a fixed ratio.
View all units & their values
| Unit | Symbol | Value | Mainly used |
|---|---|---|---|
| Degree | ° | 1 | Everyday angles |
| Radian | rad | 57.29578 | Maths, physics, SI |
| Gradian | grad | 0.9 | Surveying |
| Arcminute | ′ | 0.016667 | 1/60 of a degree |
| Arcsecond | ″ | 0.000278 | 1/3600 of a degree |
| Turn | turn | 360 | Full revolution |
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The formula
Each unit has a fixed value in degrees, so converting goes through the degree once:
Conversion
result = value × factor_from ÷ factor_toWhere:
- value = the number you typed
- factor_from = the “from” unit’s value in degrees
- factor_to = the “to” unit’s value in degrees
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Worked example
Convert 90 degrees to radians.
Step 1 · The factor
1 rad = 57.29578°Step 2 · Divide
90 ÷ 57.29578 = 1.5708 radSo 90° is π/2 ≈ 1.5708 radians.
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The units in this example
Degreesymbol: °
The everyday unit of angle; a full circle is 360°.
Common angle conversions
- 180° = π rad
- 90° = 1.5708 rad
- 1° = 0.01745 rad
- 360° = 1 turn
Radiansymbol: rad
The SI unit of angle; the angle subtending an arc equal to the radius.
Common angle conversions
- 1 rad = 57.296°
- π rad = 180°
- 2π rad = 360°
- 1 rad = 63.66 grad
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FAQ
QWhat is 90 degrees in radians?
Ninety degrees is π/2, about 1.5708 radians.
QHow do I convert degrees to radians?
Multiply the degrees by π/180 (about 0.01745).
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