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DMS to Decimal Converter – degrees minutes seconds

Quick answer

This calculator converts DMS to decimal degrees: 40°30′36″ = 40.51°.

  • Free converter with radians and gradians output and the exact formula.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How the DMS-to-Decimal Converter Works

decimal degrees = D + M/60 + S/3600

Each minute is 1/60 of a degree and each second 1/3600, so the converter sums D + M/60 + S/3600 to produce decimal degrees — the format GPS receivers, GIS software and mapping APIs expect. The same value is also expressed in radians (decimal × π/180) for mathematics and in gradians (decimal × 200/180) for surveying. Example: 40°30′36″ = 40 + 0.5 + 0.01 = 40.51°.

  1. 1

    Step 1

    Enter the degrees

  2. 2

    Step 2

    Enter the minutes (0–59)

  3. 3

    Step 3

    Enter the seconds (0–59.999)

  4. 4

    Step 4

    Read decimal degrees, radians and gradians

Use Cases

Geocaching and GPS waypoint entry

Converting survey charts for GIS software

Trigonometry homework in radians

FAQs

How do I convert 40°30′36″ to decimal?

40 + 30/60 + 36/3600 = 40.51°. The minutes add half a degree and the seconds one hundredth.

Why do GPS coordinates use decimal degrees?

Software finds decimals easier to store and compare. Human-readable charts stick to DMS, so the conversion bridges the two.

How many radians is 180°?

π radians ≈ 3.14159. Radians multiply decimal degrees by π/180 and dominate calculus and physics.

What are gradians?

A surveying unit with 400 gradians in a full circle, so 180° = 200 gon. France and some total stations still use it.