HomeConvertersNumber systemsDecimal degrees to DMS
Number conversion

Decimal degrees to DMS

Convert decimal degrees to degrees, minutes, seconds. Free online tool — no sign-up. Clear formulas and worked examples. Runs locally in your browser.

Instant result
Result
—

Enter values to convert.

Inputs —
Mode —
Formula —

Formulas

Core equations used by this converter.

dd = integer(dd)
mm = integer((dd − d) × 60)
ss = (dd − d − m/60) × 3600
Formulas = ((dd − d) × 60 − m) × 60
iDMS uses 1° = 60′ = 3600″. Extract whole degrees, then minutes, then seconds from the fractional remainder. Carry carefully when rounding seconds.

How to use

1

Extract whole degrees

Degrees d = integer part of decimal degrees dd (use |dd| first if signed).

2

Convert fraction to minutes

Multiply the fractional part by 60; the whole number is minutes m.

3

Convert remainder to seconds

Multiply the leftover fraction of minutes by 60 for seconds s; reapply sign or N-S/E-W.

Example conversions

Common values with formula and result.

ϟ

30.263888889°

30.263888889°

d = 30°
30° 15′ 50″
ϟ

45.5°

45.5°

d = 45°, m = 30′, s = 0″ → 45° 30′ 0″
45° 30′ 0″
ϟ

1.01°

1.01°

d = 1°, fraction 0.01
1° 0′ 36″

Decimal degrees to DMS specification

Version 1.1.0 · Engine tested

Calculation status
  • Engine tested 3 published cases
  • Named expert review Not performed
  • Calculation version 1.1.0

Review policy

Definition
**Decimal degrees** store an angle as one real number. **DMS** splits it into degrees, minutes, and seconds for maps, deeds, and classic navigation displays.
What it calculates
Convert decimal degrees to degrees, minutes, seconds. Extract d, then m = floor(frac×60), s = remaining×3600. Examples and FAQ.
Inputs
  • Values required by the selected conversion mode
Outputs
  • Converted result in the target unit or format
Formula
d = integer(dd) · m = integer((dd − d) × 60) · s = (dd − d − m/60) × 3600
Decimal degrees → DMS chart
Decimal degreesDMS
0.5°0° 30′ 0″
15°15° 0′ 0″
30.263889°30° 15′ 50″
45.5°45° 30′ 0″
90°90° 0′ 0″
Assumptions
  • Conversion runs locally in the browser; values are not uploaded.
  • Uses the formulas documented on this page.
Units
  • d
  • m
  • s
Boundary conditions
  • Empty or invalid input yields no valid result.
  • Out-of-range values may be rejected by the tool runtime.
Example
30.263888889° → 30° 15′ 50″
Validation cases
  • 30.263888889° → 30° 15′ 50″
  • 45.5° → 45° 30′ 0″
  • 1.01° → 1° 0′ 36″
Sources
  • CalculatorX converter runtime
  • Standard unit / encoding definitions where applicable
Calculation version
1.1.0

Background

Interpretation and common distinctions.

Use the converter tabs to switch direction when available. Results for Decimal degrees to DMS update locally in your browser.

dms DMS to decimal degrees › degr Degrees to radians › radi Radians to degrees ›

Frequently asked questions

Key distinctions behind the conversion.

How do you convert decimal degrees to DMS?

Use d = integer(dd), m = integer((dd − d) × 60), s = ((dd − d) × 60 − m) × 60. Example: 30.263888889° → 30° 15′ 50″.

How should I round seconds?

Survey work may round to 0.01″ or whole seconds. Rounding can carry into minutes and degrees — check your field standard.

How do I convert DMS back to decimal?

Switch to the DMS → decimal tab or use dd = d + m/60 + s/3600 on the reverse converter.

Does this run online or locally?

Calculation runs locally in your browser. Values are not uploaded.