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Conversions

Decimal Degrees to DMS

Convert decimal degrees. Free online Decimal Degrees to DMS. Calculate decimal degrees to dms online — fast, accurate, mobile-friendly, no signup needed.

DMS
45° 30′ 44.28″

Derivation

  1. ├── 01Givendd = 45.5123
  2. ├── 02Formula{let t=e.dd;const a=t<0?"-":"",n=|t|,r=floor(n),o=60 × (n-r),l=floor(o),i=60 × (o-l);return"".concat(a).concat(r,"\xb0 ").concat(l,"\u2032 ").concat(i.toFixed(2),"\u2033")}
  3. ├── 03Substitute{let t=e.45.5123;const a=t<0?"-":"",n=|t|,r=floor(n),o=60 × (n-r),l=floor(o),i=60 × (o-l);return"".concat(a).concat(r,"\xb0 ").concat(l,"\u2032 ").concat(i.toFixed(2),"\u2033")}
  4. └── 04Compute DMS—
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§01What is

Understanding the Decimal Degrees to DMS

The Decimal Degrees to DMS computes DMS from 1 input: decimal degrees. Convert decimal degrees.

Quick calculators for the math that shouldn’t need a notepad — instant, accurate, private to your browser. The Decimal Degrees to DMS sits in that toolkit — it convert decimal degrees. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

{let t=e.dd;const a=t<0?"-":"",n=|t|,r=floor(n),o=60 × (n-r),l=floor(o),i=60 × (o-l);return"".concat(a).concat(r,"\xb0 ").concat(l,"\u2032 ").concat(i.toFixed(2),"\u2033")}

Where

dd
Decimal degrees
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Decimal degrees = 45.5123.

  1. 01Start by noting the input — Decimal degrees: 45.5123.
  2. 02Substitute these values into the formula: {let t=e.dd;const a=t<0?"-":"",n=|t|,r=floor(n),o=60 × (n-r),l=floor(o),i=60 × (o-l);return"".concat(a).concat(r,"\xb0 ").concat(l,"\u2032 "…
  3. 03Compute DMS: the calculator returns 45° 30′ 44.28″.
  4. 04Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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