Convert degree to radian.
deg to rad — formula, reference values, and a live converter.
Convert degree (deg) to radian (rad). This is a fixed-ratio conversion — multiply the input by the factor below.
Formula
rad = deg × 0.0174533
Reference values
| deg (degree) | rad (radian) |
|---|---|
| 1 deg | 0.017453 rad |
| 5 deg | 0.087266 rad |
| 10 deg | 0.17453 rad |
| 100 deg | 1.7453 rad |
| 1000 deg | 17.453 rad |
| 10000 deg | 174.53 rad |
Things to watch for
- 1 radian = 180/π degrees ≈ 57.2958°. Radians are the 'natural' unit for math; degrees are more intuitive for everyday use.
- 1 turn = 360° = 2π rad = 400 grad (gradians, mostly historical/surveying).
- 1 degree = 60 arcminutes = 3600 arcseconds. Used in astronomy and precise surveying.
What is a degree?
One degree equals exactly 1/360 of a full circle. Geometry, navigation, surveying, and most everyday angle measurement.
What is a radian?
One radian equals the angle subtended by an arc equal in length to the radius — about 57.3 degrees. A full circle is exactly 2π radians. Mathematics, physics, computer graphics, and any calculation involving trigonometric functions.
Real-world examples of °
Here are a few familiar reference points to gauge the unit.
- 90 ° — a right angle.
- 180 ° — a straight line — half a circle.
- 360 ° — a full circle.
How to convert degree to radian
To convert a value from degree (°) to radian (rad), apply the conversion factor shown in the formula above. The calculation is the same whether you do it by hand, in a spreadsheet, or with the live converter on this page.
Steps:
- Take your input value in °.
- Apply the formula
rad = deg × 0.0174533. - The result is your value in rad.
For repeated calculations, save the formula in a spreadsheet or use the live converter at the top of this page — it handles the math automatically and displays the result as you type.
Frequently asked questions
How do I convert ° to rad?
Apply the formula ° → rad shown above, or just type your value into the converter at the top of this page. The result updates instantly.
Which is bigger, ° or rad?
This depends on the conversion ratio in the formula. If the factor multiplied by your value gives a larger number, then rad is the smaller unit (so it takes more of them to express the same quantity). If the result is smaller, then rad is the larger unit.
When would I use ° versus rad?
Both units measure angle, so the choice depends on context. Degree is typically used for geometry, navigation, surveying, and trigonometry; radian similarly. Most professional fields standardize on one or the other based on regional conventions or technical tradition.
How precise is this ° to rad conversion?
The conversion factor shown is the internationally defined exact value (or the best-published approximation if the relationship is irrational, like degrees-to-radians). The live converter on this page uses double-precision floating-point math, accurate to about 15 significant digits — far beyond any practical engineering need.
Is the conversion ratio exact, or an approximation?
Most unit conversions between SI metric units, and between SI and US customary units, have been formally defined as exact values since the 1959 international yard-pound agreement and subsequent SI redefinitions. Exceptions are unit pairs that involve irrational numbers (radians, e.g.) or empirical conversions (like food calories, which depend on temperature). When in doubt, consult the formula at the top of this page.