Angle Converter

Value

From

Result

Result1.570796

The conversion every trigonometry function needs

Convert degrees to radians for trigonometry, or into gradians, turns, arcminutes and arcseconds for surveying and astronomy.

Most programming languages and scientific calculators expect radians, while almost everyone thinks in degrees. That mismatch is behind a large share of wrong trigonometry results.

The relationship is fixed: π radians is 180 degrees. So 90° is π/2, about 1.5708 — a number worth recognising on sight.

What this calculator shows

Conversion across six angle units
Degrees and radians for everyday trigonometry
Gradians, turns and arcminutes for surveying and astronomy

What to keep in mind

A full turn is 360 degrees, 2π radians or 400 gradians.
Arcminutes and arcseconds subdivide the degree by 60 and 3600.

FAQs

Why does mathematics prefer radians?

Because they make the calculus clean. The derivative of sin(x) is cos(x) only in radians; in degrees a conversion factor appears everywhere.

How do I convert degrees to radians by hand?

Multiply by π/180. So 45° is 45π/180 = π/4, roughly 0.785.

What is a gradian?

A metric-style angle where a right angle is exactly 100 units and a full turn is 400. Surveying still uses it; almost nothing else does.

Where are arcseconds used?

Astronomy and precision optics. One arcsecond is 1/3600 of a degree — roughly the width of a coin seen from four kilometres away.

Worked example

A right angle

Input: 90 degrees → radians

Output: 1.5708 rad

Note: That is π/2. If a sine function returns 0.894 instead of 1 for 90, it is reading your number as radians.

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