How do you convert degrees to radians?

Multiply degrees by pi divided by 180. For example, 90 degrees times pi divided by 180 equals pi divided by 2, which is approximately 1.5708 radians. To convert radians to degrees, multiply by 180 divided by pi.

What is a gradian (grad)?

A gradian, also called a grad or gon, divides the full circle into 400 equal parts instead of 360 degrees. One grad equals 0.9 degrees and pi divided by 200 radians. Right angles are exactly 100 grads. Gradians are used in surveying and some European engineering traditions.

Angle Converter

Angles appear in every branch of science, engineering, and mathematics, but they are expressed in several different units depending on the discipline and the country. The degree is the most familiar unit, dividing a full circle into 360 equal parts based on ancient Babylonian mathematics. The radian is the SI unit and is preferred in physics, calculus, and computer programming because it makes many mathematical formulas simpler: the arc length of a circle equals the radius times the angle in radians, and the derivatives of trigonometric functions are clean expressions only when the angle is in radians. The gradian, also called a grad or gon, divides the full circle into 400 parts and was promoted as a metric alternative to degrees because a right angle becomes exactly 100 grads. It is still used in surveying across parts of Europe. The turn, also called a revolution or cycle, expresses the angle as a fraction of a complete rotation: one turn equals 360 degrees or 2 pi radians. Arcminutes and arcseconds are sub-divisions of the degree used in astronomy, navigation, and geodesy, where very precise angular measurements are needed: one degree equals 60 arcminutes, and one arcminute equals 60 arcseconds. This converter supports all six units. Select the unit you want to convert from, enter the angle, and all five other units update immediately.

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Convert from

Angle value

1.5708 rad

radians

Degrees90.0000 °

Gradians100.0000 grad

Turns0.2500 turns

Arcminutes5,400 ′

Arcseconds324,000 ″

How it works

All conversions use degrees as the internal base. Conversion factors to degrees: 1 rad = 180/pi degrees; 1 grad = 0.9 degrees; 1 turn = 360 degrees; 1 arcminute = 1/60 degree; 1 arcsecond = 1/3600 degree. The input is converted to degrees first, then to each other unit: radians = degrees times pi/180; gradians = degrees times 400/360; turns = degrees/360; arcminutes = degrees times 60; arcseconds = degrees times 3600.

Worked example

Convert 90 degrees to all units. Radians = 90 times pi/180 = 1.5708 rad. Gradians = 90 times 400/360 = 100 grad. Turns = 90/360 = 0.25 turns. Arcminutes = 90 times 60 = 5,400 arcmin. Arcseconds = 90 times 3600 = 324,000 arcsec. These match the default values displayed when the calculator loads with 90 degrees as the input.

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