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Angle Converter

Convert degrees, radians, gradians, turns, arcminutes and arcseconds.

By CalcHub Editorial · Last reviewed

Quick answer

  • Formula: Result = Value × (factor of from-unit in degrees) ÷ (factor of to-unit in degrees); 1 rad = 180/π °
  • Worked example — Converted angle: 3.141593 (full example below).

Angle Converter

Worked example result
Converted angle3.141593
Summary180 ° = 3.141593 rad

180 degrees is exactly π radians (3.14159265…) — a half turn.

Diagram: how the Angle Converter works — you enter Angle, From, To; it applies the formula Result = Value × (factor of from-unit in degrees) ÷ (factor of to-u…; and the worked example gives Converted angle: 3.141593.
How the Angle Converter works — the inputs, the formula, and a worked example (Converted angle: 3.141593).

Convert angles between the units used in maths, surveying and astronomy. A full turn is 360 degrees, 2π radians or 400 gradians; each degree splits into 60 arcminutes and each arcminute into 60 arcseconds.

Radians dominate mathematics because they make calculus clean (the derivative of sin x is cos x only in radians); gradians survive in European surveying.

The formula

Result = Value × (factor of from-unit in degrees) ÷ (factor of to-unit in degrees); 1 rad = 180/π °

Worked example

180 degrees is exactly π radians (3.14159265…) — a half turn.

Worked example for the Angle Converter: with Angle 180, From Degrees (°), To Radians (rad), the result is Converted angle: 3.141593; Summary: 180 ° = 3.141593 rad.
The worked example, with the example values entered and the results they give.

The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.

Frequently asked questions

How do I convert degrees to radians?

Multiply by π/180. For example, 90° = π/2 ≈ 1.5708 rad, and a right angle in gradians is exactly 100 gon.

How many arcseconds are in a degree?

3600 — 60 arcminutes per degree × 60 arcseconds per arcminute. Astronomers use arcseconds for star positions and telescope resolution.

Where are gradians used?

Surveying and some European instrumentation: a right angle is a round 100 gon, which makes slope and bearing arithmetic decimal-friendly.

Category: Unit Conversions calculators

Sources & methodology

This calculator applies the formula shown on this page exactly as written, using the standard definitions for its inputs. Results are computed from the values you enter — no data is stored — and are rounded only for display.

Content last reviewed by CalcHub Editorial.

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