Decimal to Degrees Calculator: Convert Easily

This calculator converts a decimal degree value (such as 45.525° or -122.674°) into degrees, minutes, and seconds (DMS) — the format used in mapping, navigation, and surveying. You enter the decimal degrees, and the calculator returns the equivalent DMS value, plus the separate degree, minute, and second components. It also shows the conversion formula and a worked example so you can verify the result or do the math by hand.

Formula

The conversion follows the standard base-60 method:

• Degrees (°) = the integer part of the decimal degrees (floor of the value).
• Minutes (‘) = the integer part of (decimal part × 60).
• Seconds (“) = the fractional part of the minutes × 60.

In symbols, given a decimal degree value D:

D° = floor(D)

M’ = floor((D − floor(D)) × 60)

S” = ((D − floor(D)) × 60 − M) × 60

All variables are in degrees (for D), minutes (for M), and seconds (for S). The result is conventionally written as D° M’ S” (e.g., 45° 31′ 30″).

Worked Example

Take the default value from the calculator: 45.525°.

1. Degrees: floor(45.525) = 45°
2. Decimal part: 45.525 − 45 = 0.525
3. Minutes: floor(0.525 × 60) = floor(31.5) = 31′
4. Remaining decimal: 31.5 − 31 = 0.5
5. Seconds: 0.5 × 60 = 30″

So 45.525° = 45° 31′ 30″. The calculator’s first output shows exactly that (with seconds rounded to 1 decimal).

When to Use This Conversion

Decimal degrees are the default in most GPS devices and mapping software (like Google Maps or GIS programs). However, many printed maps, nautical charts, and land survey records still use degrees, minutes, and seconds. You might need to convert:

• When entering coordinates into a GPS that only accepts DMS format.
• When reading a property boundary from a deed or survey plat.
• When communicating a location to someone using a paper map or a marine chart.
• When working with astronomical coordinates (Right Ascension and Declination are often in DMS).

Always check which format your device or document expects—entering DMS where decimal degrees are required (or vice versa) can place you miles off target.

How to Read the Result

The DMS output is read as: degrees (°) minutes (‘) seconds (“). For example, 45° 31′ 30″ means 45 degrees, 31 minutes, and 30 seconds. One degree equals 60 minutes, and one minute equals 60 seconds, so the seconds value will always be between 0 and 59.999…, and the minutes between 0 and 59.

Note that the calculator handles negative values (south or west coordinates) by keeping the negative sign on the degrees; the minutes and seconds are still positive. For instance, −122.674° becomes −122° 40′ 26.4″ (the negative applies to the whole angle).

Common Mistakes and Pitfalls

• Mixing up the sign: A negative decimal degree means the coordinate is west (longitude) or south (latitude). Do not drop the negative sign when converting.
• Rounding too early: If you round the minutes before computing seconds, you may lose precision. Always keep the full decimal until the final step.
• Forgetting that minutes and seconds max out at 60: If you get 75 seconds, that’s actually 1 minute and 15 seconds—you must carry over.
• Using the wrong base: Decimal degrees are base-10, but DMS is base-60. Multiplying the decimal part by 60 (not 100) is essential.

Limits of the Formula

This conversion is purely mathematical and works for any real number. However, it does not account for map datums or coordinate systems (like WGS84 vs. NAD83). The same decimal value can represent slightly different physical locations depending on the datum used. For high-precision surveying or navigation, always confirm the datum. Also, the calculator rounds seconds to one decimal place, which is sufficient for most purposes but may not be exact for geodetic work requiring sub-second accuracy.

Alternatives to a Calculator

If you don’t have a calculator handy, you can convert manually using the same steps shown above. Many GPS units and mapping apps also have a built-in coordinate format setting that lets you display DMS directly. Spreadsheet software (like Excel or Google Sheets) can be set up with a formula: for example, =TEXT(A1/24, "[h]° mm' ss\"") works in Excel if A1 contains decimal degrees. But for a quick, error-free conversion, a dedicated calculator like this one is the simplest option.

Frequently Asked Questions

What is the difference between decimal degrees and degrees/minutes/seconds?
Decimal degrees express an angle as a single number (e.g., 45.525°), while DMS breaks it into degrees, minutes, and seconds (e.g., 45° 31′ 30″). Both represent the same angle; they are just different notations.

How do I convert DMS back to decimal degrees?
Divide the seconds by 3600, divide the minutes by 60, and add both to the degrees. For example, 45° 31′ 30″ = 45 + 31/60 + 30/3600 = 45.525°.

Why are there 60 minutes in a degree?
Degrees, minutes, and seconds come from the ancient Babylonian sexagesimal (base-60) number system, which is still used for angles and time. It allows for easy division by 2, 3, 4, 5, and 6.

What if my decimal degrees have more than three decimal places?
The calculator handles any number of decimals. The seconds output is rounded to one decimal place, which is accurate to about 30 meters on the Earth’s surface. For higher precision, you can use the raw seconds value (not rounded) in your own calculations.

Does this work for negative coordinates?
Yes. The calculator keeps the negative sign on the degrees, and the minutes and seconds are computed from the absolute value of the fractional part. For example, −122.674° becomes −122° 40′ 26.4″.

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in dd | Decimal degrees | ° | 45.525 | 0
out dms | Degrees, minutes, seconds | ° ' " | floor(dd) + "° " + floor((dd - floor(dd)) * 60) + "' " + round(((dd - floor(dd)) * 60 - floor((dd - floor(dd)) * 60)) * 60, 1) + "\"" | 0
out deg | Degrees | ° | floor(dd) | 0
out min | Minutes | ' | floor((dd - floor(dd)) * 60) | 0
out sec | Seconds | " | ((dd - floor(dd)) * 60 - floor((dd - floor(dd)) * 60)) * 60 | 1