Angles Converter

Convert between angle units. Exact factors, a quick reference table and worked examples.

180 ° = 3.141593 rad

The same value in every unit

UnitSymbolValue
Degree°180
Radianrad3.141593
Milliradianmrad3 141.593
Gradiangrad200
Turn (revolution)turn0.5
Arcminute′10 800
Arcsecond″648 000

How to convert angles units

Every angles unit is related to one base unit (Radian, rad) by an exact factor. To convert, multiply by the factor of the unit you start from and divide by the factor of the unit you want.

value in new unit = value × (factor of old unit ÷ factor of new unit)

For example, 1 ° = 0.01745329 rad and 1 rad = 1 rad, so 1 ° = 0.01745329 rad.

Quick reference table

How many of the units in the column headings make up one of the unit in each row.

One…= °= rad= mrad= grad= turn= ′
1 °10.0174532917.453291.1111110.00277777860
1 rad57.2957811 00063.661980.15915493 437.747
1 mrad0.057295780.00110.063661980.00015915493.437747
1 grad0.90.0157079615.7079610.002554
1 turn3606.2831856 283.185400121 600
1 ′0.016666670.00029088820.29088820.018518524.62963 × 10⁻⁵1
1 ″0.00027777784.84814 × 10⁻⁶0.0048481370.0003086427.71605 × 10⁻⁷0.01666667

Common values: ° to rad

Degree (°)Radian (rad)
1 °0.01745329 rad
2 °0.03490659 rad
5 °0.08726646 rad
10 °0.1745329 rad
20 °0.3490659 rad
50 °0.8726646 rad
100 °1.745329 rad
200 °3.490659 rad
500 °8.726646 rad
1 000 °17.45329 rad

Worked examples

Convert 180 ° to rad

  • 1 ° = 0.01745329 rad and 1 rad = 1 rad.
  • 180 × 0.01745329 ÷ 1 = 3.141593 rad.

Convert 50 mrad to °

  • 1 mrad = 0.001 rad and 1 ° = 0.01745329 rad.
  • 50 × 0.001 ÷ 0.01745329 = 2.864789 °.

Convert 250 ″ to rad

  • 1 ″ = 4.84814 × 10⁻⁶ rad and 1 rad = 1 rad.
  • 250 × 4.84814 × 10⁻⁶ ÷ 1 = 0.001212034 rad.

The units explained

UnitSymbolExact factorWhere it is used
Degree°1 ° = 0.01745329 radEveryday use, drawings, machining
Radianrad1 rad = 1 radMathematics, physics, programming
Milliradianmrad1 mrad = 0.001 radOptics, small tilts
Gradiangrad1 grad = 0.01570796 radSurveying
Turn (revolution)turn1 turn = 6.283185 radRotation counts, motors
Arcminute′1 ′ = 0.0002908882 radNavigation, fine angles
Arcsecond″1 ″ = 4.84814 × 10⁻⁶ radAstronomy, precision surveying

Key facts

  • π rad = 180°, so 1 rad ≈ 57.2958° and 1° ≈ 0.0174533 rad.
  • Arc length s = r × θ, with θ in radians. Math functions in most languages use radians.
  • A full turn is 360° = 2π rad = 400 gradians.

FAQ

How many Radian units are in one Degree?

1 ° = 0.01745329 rad.

How do I convert ° to rad?

Multiply by 0.01745329 (the factor 0.01745329 ÷ 1). To go back, divide by 0.01745329 or multiply by 57.29578.

What is the degree (°) used for?

Everyday use, drawings, machining.

What is the radian (rad) used for?

Mathematics, physics, programming.

Are the conversion factors exact?

Where a unit is defined exactly (the inch is 25.4 mm, the pound is 0.45359237 kg, standard gravity is 9.80665 m/s²) the factor is exact; others are given to ten or more digits. Results are shown to seven significant digits.

References

  • NIST Special Publication 811, Guide for the Use of the International System of Units (SI), and NIST Handbook 44, Appendix C (general tables of units of measurement).
  • BIPM, The International System of Units (SI Brochure), 9th edition; ISO 80000 (quantities and units).

Last reviewed: November 2026.