Angle Converter
Convert between degrees, radians, gradians and turns.
What the Angle Converter does
A full circle is 360 degrees, 2π radians, 400 gradians or one turn. Radians are the natural unit for calculus and trigonometry because the arc length of a unit circle equals the angle itself.
Formula
Convert to degree, then divide by the target unit's factorResult = Value × (from factor ÷ to factor)
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| Value | number | Yes | — |
| From | one of 7 options | Yes | — |
| To | one of 7 options | Yes | — |
How to use it
- Choose From and To.
- Enter Value.
- Select Calculate.
Worked example
Convert 90 degrees to radians.
- Value
- 90
- From
- Degree
- To
- Radian
90 × π/180 = 1.5708 rad, which is π/2.
Reading the result
- A full turn is 360 degrees, 2π radians, 400 gradians or 1 turn. A right angle is 90 degrees, π/2 radians or 100 gradians.
- An arcminute is a sixtieth of a degree and an arcsecond a sixtieth of that, which is the resolution surveying and astronomy work at.
Common mistakes
- Passing degrees to a trigonometric function. Nearly every programming language expects radians, so sin(30) returns −0.988 instead of 0.5.
- Confusing this mil with a thousandth of an inch. The angular mil used here is roughly 1/6400 of a turn.
Frequently asked questions
Why use radians?
Trigonometric derivatives and series only take their simple forms in radians. Most programming languages expect radians in their sin and cos functions.