Case 1
- Angle to convert
- 180
- From unit
- Degree (°)
- To unit
- Radian (rad)
3.141593
Open with these valuesAngle Converter
3.141593
Result: 3.141593Angle units are plain multiples of the degree: a radian is 180 ÷ π degrees, a gon exactly 0.9°, an arcminute a sixtieth of a degree, an arcsecond a 3600th, and a turn 360°. So 180° is π radians and a right angle is exactly 100 gon.
Most-used pairs
each is its own pageDegrees to radians1° = 0.017453 radRadians to degrees1 rad = 57.29578°Degrees to gon1° = 1.111111 gonGon to degrees1 gon = 0.9°Degrees to arcminutes1° = 60′Degrees to arcseconds1° = 3600″Turns to degrees1 turn = 360°
All 6 units
| Unit | Symbol | In ° | Typical use |
|---|---|---|---|
| Degree | ° | 1 | Everyday angles, 360 in a circle |
| Radian | rad | 57.295779513 | Maths, physics, programming |
| Gradian (gon) | gon | 0.9 | Surveying, 400 in a circle |
| Arcminute | ′ | 0.016666667 | Navigation and astronomy |
| Arcsecond | ″ | 0.000277778 | Telescope resolution, parallax |
| Turn | turn | 360 | Full revolutions, rotation counts |
Degree to Radian
prints complete- 1 °
- 0.017453 rad
- 2 °
- 0.034907 rad
- 3 °
- 0.05236 rad
- 4 °
- 0.069813 rad
- 5 °
- 0.087266 rad
- 6 °
- 0.10472 rad
- 7 °
- 0.122173 rad
- 8 °
- 0.139626 rad
- 9 °
- 0.15708 rad
- 10 °
- 0.174533 rad
- 11 °
- 0.191986 rad
- 12 °
- 0.20944 rad
- 13 °
- 0.226893 rad
- 14 °
- 0.244346 rad
- 15 °
- 0.261799 rad
- 16 °
- 0.279253 rad
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Worked examples
Case 2
- Angle to convert
- 90
- From unit
- Degree (°)
- To unit
- Gradian / gon (gon)
100.000000
Open with these valuesCase 3
- Angle to convert
- 1
- From unit
- Turn / revolution (turn)
- To unit
- Degree (°)
360.000000
Open with these valuesHow it's calculated
result = value × (degrees per from-unit) ÷ (degrees per to-unit)
- StepEnter the angle you already have.
- StepChoose the unit it is written in under From unit.
- StepChoose the unit you want under To unit.
- ResultRead the result — it is already in the unit you chose.
Reference table
| One unit | Expressed in | Exact factor |
|---|---|---|
| 1 rad | ° | 57.295780 |
| 1 gon | ° | 0.9 |
| 1 turn | ° | 360 |
| 1 ′ | ° | 0.016667 |
| 1 ″ | ° | 0.000278 |
Questions
How do I convert one angle unit to another?
Enter your value, choose the unit you have under From unit and the unit you want under To unit. The value is turned into degrees first and then into the target unit, so degrees, radians, gon, arcminutes, arcseconds and turns all convert in one step.
How do I convert degrees to radians?
Multiply the degree value by π ÷ 180, about 0.0174533. The cleanest anchor is 180° = π rad ≈ 3.141593 rad, so a full circle of 360° is 2π rad. To go the other way, multiply radians by 180 ÷ π ≈ 57.29578.
What is a radian, and why do mathematicians use it?
A radian is the angle at which the arc length equals the radius, which makes it the natural unit — calculus formulas only come out clean in radians. A full turn is 2π rad ≈ 6.283185 rad, half a turn is π rad, and a right angle is π ÷ 2 rad.
What is a gradian (gon)?
A gradian — also called gon or new degree — splits the full circle into 400 parts instead of 360, so a right angle is exactly 100 gon. It is used mainly in surveying and some European engineering, where the round number simplifies slope and bearing work.
What are arcminutes and arcseconds?
They subdivide the degree the way minutes and seconds subdivide an hour: 1° is 60 arcminutes and 3600 arcseconds. Astronomers and navigators use them for tiny angles — the full Moon spans about 30 arcminutes.
Sources and last check
Information, not professional advice.