How do I convert degrees to radians?

Multiply degrees by π/180. For example, 90° × π/180 = π/2 rad.

Gradians (or gons) divide a right angle into 100 grads, so one full turn is 400 grads. To convert degrees to gradians, multiply by 10/9.

How do I convert DMS (degrees, minutes, seconds) to decimal degrees?

Use decimal degrees = degrees + minutes/60 + seconds/3600. The converter above does this automatically.

Angle Converter: Degrees, Radians, Gradians, DMS & Turns

Degrees (°)	Radians (rad)	Gradians	Turns
30	π/6 ≈ 0.5236	33.3333	0.08333
45	π/4 ≈ 0.7854	50	0.125
90	π/2 ≈ 1.5708	100	0.25
180	π ≈ 3.1416	200	0.5
360	2π ≈ 6.2832	400	1

Angle conversion formulas

Degrees to radians: rad = deg × π / 180

Radians to degrees: deg = rad × 180 / π

Degrees to gradians: grad = deg × 10 / 9

Gradians to degrees: deg = grad × 0.9

Degrees to turns: turn = deg / 360

DMS to decimal degrees: deg = D + M/60 + S/3600

When to use each unit

Degrees (°): human-friendly, geometry, navigation.
Radians (rad): calculus, trigonometric functions in programming and math libraries.
Gradians (gons): surveying and some European engineering contexts (right angle = 100 gons).
Turns: animations, rotations in graphics, helpful when thinking in full revolutions.
DMS: location, bearings, legacy measurements.

FAQ

1. Why does my calculator need radians?

Most math functions (sin, cos, tan) are defined in radians, so scientific calculators and programming languages expect radians by default.

2. Are gradians the same as gons?

Yes. “Grad”, “gon”, and “grade” are used interchangeably for the 400-based angle system.

3. How do I format negative angles in DMS?

Convert the absolute value to DMS, then apply the sign back. The tool above assumes positive angles for DMS, which is typical in surveying tables.

Full original guide (expanded)

Add here extra examples: converting bearings, comparing survey readings, converting robot joint rotations or CSS transforms to degrees.

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

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Formula (extracted text)

Degrees to radians: rad = deg × π / 180 Radians to degrees: deg = rad × 180 / π Degrees to gradians: grad = deg × 10 / 9 Gradians to degrees: deg = grad × 0.9 Degrees to turns: turn = deg / 360 DMS to decimal degrees: deg = D + M/60 + S/3600

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
NIST — SI units — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/owm/metric-si/si-units

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
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