Quick answer
To convert angles, multiply by the ratio of the unit factors. 180 degrees equals π radians, which is 3.1416 rad. A full turn is 360° = 2π rad = 400 gradians.
Enter the value, choose the units and the decimal places. The calculator returns the converted angle.
Related tools: Reference Angle Calculator: Acute angle between the terminal side and the x-axis. Coterminal Angle Calculator: Angles sharing the same terminal side. Angle of Elevation Calculator: Angle of elevation from a height difference and horizontal distance.
How to use the Angle Converter
- Enter value.
- Choose from: Degree (°), Radian (rad), Milliradian (mrad), Gradian (grad), Arcminute (′) and Arcsecond (″) and 1 more.
- Choose to: Degree (°), Radian (rad), Milliradian (mrad), Gradian (grad), Arcminute (′) and Arcsecond (″) and 1 more.
- Enter decimal places (between 0 and 10). It starts at 4.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Value | A number | — |
| From | Choose one: Degree (°); Radian (rad); Milliradian (mrad); Gradian (grad); Arcminute (′); Arcsecond (″); Turn (revolution) | Starts at Degree (°) |
| To | Choose one: Degree (°); Radian (rad); Milliradian (mrad); Gradian (grad); Arcminute (′); Arcsecond (″); Turn (revolution) | Starts at Radian (rad) |
| Decimal places | A number | ≥ 0, ≤ 10, starts at 4 |
Formula and method
Formula
result = value × (factor of source ÷ factor of target), base unit: radian
IEEE-754 double precision; displayed to the chosen number of decimal places (default 4). Very small or large results are shown in scientific notation.
Every unit is defined by an exact or published factor to the base unit (radian). The value is multiplied by the source factor and divided by the target factor.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Value = 180; From = Degree (°); To = Radian (rad); Decimal places = 4.
| Result | Value |
|---|---|
| Degree (°) → Radian (rad) | 3.1416 |
| Input | 180 Degree (°) |
Example 2
Inputs: Value = 1; From = Turn (revolution); To = Degree (°); Decimal places = 4.
| Result | Value |
|---|---|
| Turn (revolution) → Degree (°) | 360 |
| Input | 1 Turn (revolution) |
Example 3
Inputs: Value = 100; From = Gradian (grad); To = Degree (°); Decimal places = 4.
| Result | Value |
|---|---|
| Gradian (grad) → Degree (°) | 90 |
| Input | 100 Gradian (grad) |
The first line is the headline result (degree (°) → Radian (rad)). Below it the angle Converter lists input, which describe the same case from other angles. IEEE-754 double precision; displayed to the chosen number of decimal places (default 4). Very small or large results are shown in scientific notation.
Unit reference
Each unit expressed in the base unit used for the calculation. Conversions go through this base unit, so any unit can be converted to any other in the table.
| Unit | Equals (in radian) |
|---|---|
| Degree (°) | 0.01745329252 |
| Radian (rad) | 1 |
| Milliradian (mrad) | 0.001 |
| Gradian (grad) | 0.01570796327 |
| Arcminute (′) | 0.0002908882087 |
| Arcsecond (″) | 0.000004848136811 |
| Turn (revolution) | 6.283185307 |
Key relationships
1 radian is 57.2958°, 1° is 0.017453 rad and 1 gradian is 0.9°. Right angles are 90°, π/2 rad or 100 grad. Arcminutes and arcseconds divide a degree by 60 and then 3,600.
Where each unit is used
Degrees are common in everyday geometry and navigation, radians in calculus and physics because they make formulas like arc length s = rθ simple, and gradians in some surveying. Negative angles are allowed and mean the opposite direction.
How the result changes with value
Holding every other input at the first worked example, this table changes only value. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Value | Degree (°) → Radian (rad) | Input |
|---|---|---|
| 90 | 1.5708 | 90 Degree (°) |
| 180 | 3.1416 | 180 Degree (°) |
| 360 | 6.2832 | 360 Degree (°) |
| 720 | 12.5664 | 720 Degree (°) |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Value: left empty shows "Enter value." beside that field and no result.
Choosing between the Angle Converter and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Reference Angle Calculator](/math/reference-angle/) | angle | Reference angle |
| [Coterminal Angle Calculator](/math/coterminal-angle/) | angle | Smallest non-negative coterminal angle |
| [Angle of Elevation Calculator](/math/angle-of-elevation-calculator/) | height difference and horizontal distance | Angle of elevation |
| [Angle of Depression Calculator](/math/angle-of-depression-calculator/) | height difference and horizontal distance | Angle of depression |
| [Double Angle Calculator](/math/double-angle-calculator/) | angle and unit | sin 2θ |
Background: unit conversion
Many customary units are defined exactly in terms of metric ones: since the 1959 International Yard and Pound Agreement an inch is exactly 2.54 cm and a pound is exactly 0.45359237 kg (NIST SP 811 lists these). So most length and mass conversions are exact apart from the rounding of the displayed result.
To convert, multiply the value by the source unit's factor to reach the base unit, then divide by the target unit's factor; the unit table on this page lists every factor used. Temperature and fuel economy are the exceptions, because they are not simple multiples.
Assumptions and limitations
- Negative values are allowed
- Zero converts to zero (except L/100 km, where zero is invalid)
- Units from different quantities cannot be converted
- Very large or tiny results switch to exponent notation
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for value to confirm this.
Frequently asked questions
How many degrees is 1 radian?
One radian is about 57.2958 degrees.
What is π/4 in degrees?
π/4 radians is 45 degrees: enter 0.7854 radians in the converter, or use 180 ÷ 4.
Does the converter support turns?
Choose the unit list entry for turns or revolutions if offered.
What does the Angle Converter calculate?
Convert degrees, radians, gradians, arcminutes and turns. It returns Degree (°) → Radian (rad) and Input.
What formula does the Angle Converter use?
result = value × (factor of source ÷ factor of target), base unit: radian. Every unit is defined by an exact or published factor to the base unit (radian).
What does the “From” option change?
It sets how the angle is worked out. The choices are Degree (°), Radian (rad), Milliradian (mrad), Gradian (grad), Arcminute (′), Arcsecond (″) and Turn (revolution).
What is an example of a angle result?
With value 180, from Degree (°), to Radian (rad) and decimal places 4, the degree (°) → Radian (rad) is 3.1416.
Where does the method come from?
The method follows: BIPM SI Brochure (9th ed.): radian; ISO 80000-3.
Related calculators
- Reference Angle Calculator — Acute angle between the terminal side and the x-axis.
- Coterminal Angle Calculator — Angles sharing the same terminal side.
- Angle of Elevation Calculator — Angle of elevation from a height difference and horizontal distance.
- Angle of Depression Calculator — Angle of depression from a height difference and horizontal distance.
- Double Angle Calculator — Double-angle identities evaluated at an angle.
- Half Angle Calculator — Half-angle identities evaluated at an angle.
- Illuminance Converter — Convert lux, foot-candles and phot.
- Luminance Converter — Convert cd/m², foot-lamberts, lamberts and more.
Sources
- BIPM SI Brochure (9th ed.): radian
- ISO 80000-3
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.