# Degrees to Radians Calculator

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

## 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: 2026-04-08