Apex Conversion

DMS to Decimal Degrees Converter

Got coordinates like 40° 26′ 46″ N from a chart or deed, but your GPS app wants a plain decimal? Convert degrees-minutes-seconds to decimal degrees — or back the other way — with the hemisphere handled for you.

Hemisphere

Decimal degrees

40.446111°

paste into any GPS app

Formatted DMS

40° 26′ 46″ N

positive in decimal form

One minute of latitude ≈ 1.15 statute miles (1 nautical mile — that's its original definition), and one second ≈ 101 ft. GPS apps and mapping APIs want decimal degrees; nautical charts, surveys, and aviation still use DMS.

Two Ways to Write the Same Spot

A minute is 1/60 of a degree and a second is 1/60 of a minute, so the conversion is decimal = degrees + minutes ÷ 60 + seconds ÷ 3,600 — negative for the southern or western hemisphere. 40° 26′ 46″ works out to 40 + 0.43333 + 0.01278 = 40.446111°. Going the other way, 73.9857° splits into 73° whole, then 0.9857 × 60 = 59.142 → 59′, then 0.142 × 60 = 8.52″ — giving 73° 59′ 8.52″. GPS apps and mapping APIs expect decimal; nautical charts, surveys, and property deeds still speak DMS.

Coordinate quick reference

decimal = deg + min/60 + sec/3600   (− for S or W)

40° 26′ 46″ N  =  40.446111°
73.9857° W     =  73° 59′ 8.52″ W   (−73.9857)

On the ground (latitude):
  1° ≈ 69 miles      1′ ≈ 1.15 mi (1 nautical mile)
  1″ ≈ 101 ft        0.0001° ≈ 36 ft

Sign convention: N and E positive, S and W negative

Frequently Asked Questions

Which way is negative longitude?

West. Longitude runs from −180° to +180° measured from the Greenwich meridian, so the entire Americas are negative — New York City is about −74.0°, Los Angeles −118.2°. Negative latitude means south of the equator. If a US coordinate pastes into a map and lands in China, you almost certainly dropped the minus sign.

How do I convert 40° 26′ 46″ N to decimal degrees?

Add the pieces: 40 + 26/60 + 46/3600 = 40 + 0.43333 + 0.01278 = 40.446111°. It stays positive because N (and E) are positive; an S or W coordinate gets a minus sign. Going the other way, multiply the leftover fraction by 60 at each step: 73.9857° → 73°, then 0.9857 × 60 = 59.142 → 59′, then 0.142 × 60 = 8.52″.

How many decimal places do GPS coordinates need?

Four decimal places pin a latitude to about 36 ft, five to about 3.6 ft, and six to about 4 inches — finer than consumer GPS can actually measure (typically 10–15 ft). Six decimals, the precision this converter outputs, is the practical maximum; anything beyond that is noise.

Why do my coordinates look like 40° 26.767′ with no seconds?

That's degrees decimal minutes (DDM), a third format that marine GPS units and geocaching use by default. Convert the minute fraction to seconds by multiplying by 60: 0.767′ × 60 = 46″, so 40° 26.767′ equals 40° 26′ 46″, which equals 40.446111° in decimal.

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