Angle Converter
Degrees to radians, gradians & revolutions — see it, not just the number
Convert angle units instantly, with a live visual gauge that draws the exact angle you type in. Built for trigonometry, physics numericals, and competitive exam prep.
Convert an angle now — free
Classic Angles — Degrees, Radians & Gradians
The angles that show up constantly in trigonometry, worth knowing by heart.
| Degrees | Radians | Decimal | Gradians |
|---|---|---|---|
| 0° | 0 | 0 | 0 grad |
| 30° | π/6 | 0.5236 | 33.33 grad |
| 45° | π/4 | 0.7854 | 50 grad |
| 60° | π/3 | 1.0472 | 66.67 grad |
| 90° | π/2 | 1.5708 | 100 grad |
| 180° | π | 3.1416 | 200 grad |
| 270° | 3π/2 | 4.7124 | 300 grad |
| 360° | 2π | 6.2832 | 400 grad |
Need an angle not listed here? Type it into the calculator above for an instant answer.
Worked Examples
See exactly how each conversion is calculated, step by step.
Convert 90° to radians.
- Multiply by π/180
- 90 × π/180
- = π/2
Convert π/2 radians to degrees.
- Multiply by 180/π
- (π/2) × 180/π
- = 180/2
Convert 180° to gradians.
- 1° = 10/9 grad, so multiply by 10/9
- 180 × 10/9
- = 1800/9
Convert 2.5 revolutions to degrees.
- 1 revolution = 360°, so multiply by 360
- 2.5 × 360
- = 900°
Try any of these with the shortcut chips in the calculator above, or swap in your own numbers.
Free Angle Converter — Degrees, Radians, Gradians & More
Angle conversion comes up throughout trigonometry, calculus, and physics — switching between degrees and radians for a formula, converting a gradian measurement from a surveying problem, or working out how many degrees a wheel turns in a given number of revolutions. This angle converter covers degrees, radians, gradians, revolutions, arcminutes and arcseconds, with results that update instantly as you type.
The conversion worth actually understanding, not just memorising, is degrees to radians: a full circle is 360° or exactly 2π radians, so 1° equals π/180 radians, and 1 radian equals 180/π degrees (about 57.3°). Because radians are defined directly from the geometry of a circle, they're the unit calculus and most higher-level physics use by default — angular velocity, angular acceleration, and trig function derivatives are all defined in terms of radians.
Gradians (also called gons) divide a right angle into 100 parts instead of 90, so a full circle is 400 gradians — this unit shows up mainly in surveying and some calculator "GRAD" modes. A revolution (or turn) is simply one full 360° rotation, useful for problems involving wheels, gears, or rotational motion.
Every conversion uses exact mathematical constants (π, not a rounded approximation), so the result you get here is accurate, not estimated. Use the live gauge above the calculator to get an intuitive feel for the angle you've entered. Need a related tool? The speed, distance and time calculator covers linear motion, or head back to the unit converter hub for everything else.
← Back to all unit convertersAngle conversion — common questions
Multiply the value in degrees by π/180. For example, 90° × π/180 = π/2 radians, approximately 1.5708.
Multiply the value in radians by 180/π. For example, π/2 radians × 180/π = 90°.
π radians equals exactly 180°, since a full circle is 360° or 2π radians, and π radians is exactly half of that.
A gradian (or gon) divides a right angle into 100 equal parts instead of 90, so a full circle is 400 gradians. 1 gradian equals 0.9 degrees, and it's mainly used in surveying.
One full revolution (or turn) equals 360 degrees, which is also exactly 2π radians or 400 gradians.
Yes. Switching between degrees and radians is constant in trigonometry, calculus and physics problems, and this converter uses exact values based on π rather than rounded approximations.