# Degrees to Radians Calculator

Convert degrees to radians with the exact formula: radians = degrees x pi/180. Also displays pi form, turns, and gradians.

## What this calculates

Convert any angle from degrees to radians using the formula radians = degrees x pi / 180. The calculator also shows the result as a fraction of pi, plus turns and gradians for engineering applications.

## Inputs

- **Angle in Degrees** (°) — Enter an angle in degrees.

## Outputs

- **Radians** (rad) — The angle in radians.
- **Pi Form** — formatted as text — The angle expressed as a fraction or multiple of pi.
- **Turns** (turns) — The angle as a fraction of a full rotation.
- **Gradians** (gon) — The angle in gradians (400 gon = 360°).

## Details

Degrees and radians are both units for measuring angles. Degrees divide a full circle into 360 parts, while radians define one full rotation as 2π (roughly 6.2832). Radians are the standard unit in mathematics and physics because they simplify many formulas.

Formula: radians = degrees x (π / 180)

Common Degree to Radian Conversions

Degrees
Radians
Pi Form

0°
0
0

30°
0.5236
π/6

45°
0.7854
π/4

60°
1.0472
π/3

90°
1.5708
π/2

120°
2.0944
2π/3

180°
3.1416
π

270°
4.7124
3π/2

360°
6.2832
2π

Why radians matter: In calculus, the derivative of sin(x) is cos(x) only when x is measured in radians. If you use degrees, extra conversion factors appear in every derivative and integral. That is why virtually all scientific and engineering software defaults to radians.

To convert back: degrees = radians x (180 / π).

## Frequently Asked Questions

**Q: What is the formula to convert degrees to radians?**

A: Multiply the degrees by pi/180 (approximately 0.01745). For example, 90 degrees = 90 x pi/180 = pi/2 radians, which is about 1.5708 radians.

**Q: Why are there 2 pi radians in a full circle?**

A: A radian is defined as the angle created when the arc length equals the radius. Since a full circle has a circumference of 2 x pi x radius, the total angle in radians is 2pi. This definition makes radians naturally connected to the geometry of a circle.

**Q: How do I convert radians back to degrees?**

A: Multiply the radians by 180/pi (approximately 57.2958). For example, pi/4 radians = (pi/4) x 180/pi = 45 degrees.

**Q: What is a gradian?**

A: A gradian (also called a gon or grade) divides a right angle into 100 parts, so a full circle is 400 gradians. They are used in some European surveying and engineering contexts. 1 gradian = 0.9 degrees = pi/200 radians.

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Source: https://vastcalc.com/calculators/conversion/degrees-to-radians
Category: Conversion
Last updated: 2026-04-21