Subtract Degrees Minutes Seconds: How-To & Examples

This calculator subtracts angles or coordinates given in degrees, minutes, and seconds (DMS). You enter the first value and the second value in DMS format, and it returns the difference in the same format, along with the result in decimal degrees. The subtraction is done by converting both values to decimal degrees, subtracting, and converting back to DMS.

Formula

The core formula converts each DMS value to decimal degrees, subtracts, then converts back. For a value D° M’ S”:

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

Then subtract: Result (decimal) = Decimal1 − Decimal2

To convert back to DMS, take the integer part as degrees, multiply the fractional part by 60 to get minutes, and the fractional part of that by 60 to get seconds.

• D – degrees (integer, can be negative for coordinates south or west)
• M – minutes (0–59, integer)
• S – seconds (0–59.999…, can be decimal)

Worked Example

Using the default values: subtract 10° 45′ 30″ from 30° 15′ 50″.

1. Convert the first angle: 30 + 15/60 + 50/3600 = 30 + 0.25 + 0.0138889 = 30.2638889°
2. Convert the second angle: 10 + 45/60 + 30/3600 = 10 + 0.75 + 0.0083333 = 10.7583333°
3. Subtract: 30.2638889 − 10.7583333 = 19.5055556°
4. Convert back: degrees = 19; fractional = 0.5055556 × 60 = 30.3333 minutes → 30′; seconds = 0.3333 × 60 = 20″

Result: 19° 30′ 20″, which matches the calculator output.

Why Subtract in DMS?

Degrees, minutes, and seconds are the traditional way to express geographic coordinates and angles in fields like surveying, astronomy, and navigation. Even though decimal degrees are easier for calculations, many maps, GPS units, and legal documents still use DMS. Subtracting DMS values directly is error-prone because of the base-60 carry/borrow rules, so converting to decimal first is the safest method.

For example, when calculating the angular distance between two stars or the difference in latitude between two points, you need the exact DMS difference, not just an approximate decimal. This calculator handles the conversion automatically, so you don’t have to worry about borrowing 60 seconds from a minute or 60 minutes from a degree.

How to Read the Result

The primary output is the difference in DMS format, e.g., 19° 30′ 20″. The second output shows the same difference in decimal degrees (19.5056°). If you are working with coordinates, a positive result means the first point is north or east of the second (depending on whether you entered latitude or longitude). A negative result means the opposite direction. For angles, the sign indicates which angle is larger.

Note that the calculator does not normalize the result to a 0–360° range. If you subtract a larger angle from a smaller one, you get a negative DMS value (e.g., −5° 10′ 0″). This is correct for many applications, but if you need a positive angle, add 360° to the result.

Common Mistakes and Pitfalls

• Forgetting base-60: When doing manual subtraction, remember that 1 degree = 60 minutes, not 100. The calculator handles this, but if you check manually, don’t treat minutes as decimals.
• Mixing formats: Ensure both inputs are in DMS, not one in decimal degrees. The calculator expects the format like 30° 15′ 50″, but it also accepts plain numbers (e.g., 30.25) as decimal degrees if you omit the symbols.
• Negative coordinates: For southern or western coordinates, the degree value is negative. The calculator treats the whole DMS as negative, so −10° 30′ 0″ is −10.5°, not −10° + 0.5°.
• Seconds precision: Seconds can be decimals (e.g., 50.5″). The calculator accepts them, but the output rounds to the nearest whole second by default. For higher precision, increase the decimal places in the output settings.

When to Use This Calculator

Use this tool whenever you need to find the difference between two angles or coordinates expressed in DMS. Common scenarios include:

• Calculating the angular separation between two celestial objects.
• Finding the difference in latitude or longitude between two map points.
• Subtracting survey measurements that use DMS notation.
• Converting a DMS value to decimal degrees for use in spreadsheets or GIS software.

For the reverse conversion (decimal to DMS), many calculators also offer that, but this one focuses on subtraction. If you only need to convert a single DMS value, you can subtract 0° 0′ 0″ to get the decimal equivalent.

Limitations of the Formula

The subtraction formula is exact and works for any real numbers, but there are a few limitations to be aware of:

• Range: The result can be any value, but for coordinates, the valid range for latitude is −90° to +90° and for longitude −180° to +180°. The calculator does not enforce these limits; it’s up to you to interpret the result correctly.
• Rounding: The DMS output rounds seconds to the nearest whole number by default. If you need sub-second precision, adjust the decimal places for the DMS output (though the calculator’s output format may only show whole seconds).
• Sign convention: The calculator always subtracts the second input from the first. If you need the absolute difference, take the absolute value of the result.

Frequently Asked Questions

How do I subtract DMS manually without a calculator?

Convert each DMS to decimal degrees by dividing minutes by 60 and seconds by 3600, then subtract. To convert back, take the integer part as degrees, multiply the decimal by 60 to get minutes, and the remaining decimal by 60 to get seconds. For example, 19.5056° → 19° + 0.5056×60 = 30.336′ → 30′ + 0.336×60 = 20.16″ → 19° 30′ 20″.

Why do I get a negative result?

Because the calculator subtracts the second value from the first. If the second is larger, the result is negative. This is correct for many uses, but if you want the absolute difference, just ignore the sign or take the absolute value.

Can I input values like 30.5° instead of 30° 30′ 0″?

Yes, the calculator accepts decimal degrees as input. If you type 30.5, it interprets it as 30.5 degrees, which is equivalent to 30° 30′ 0″. However, the output is always in DMS format, so you’ll see the result as degrees, minutes, and seconds.

Does the calculator handle negative coordinates properly?

Yes. For example, subtracting 10° 30′ 0″ from −5° 0′ 0″ gives −15° 30′ 0″, which is correct. The calculator treats the entire DMS value as negative, so −5° 0′ 0″ is −5.0°, not −5° + 0°.

What if my seconds have decimals?

The calculator accepts decimal seconds, like 30° 15′ 50.5″. The output will round to the nearest whole second by default, but you can increase the decimal places in the output settings if you need more precision.

Is this the same as subtracting angles in trigonometry?

Yes, the mathematical operation is identical. The only difference is the format. In trigonometry, you often work in decimal degrees or radians, but the subtraction is the same. This calculator just makes it easier to work with the DMS notation commonly used in navigation and astronomy.

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in dms1 | First angle (DMS) | - | 30° 15' 50" | 0
in dms2 | Second angle (DMS) | - | 10° 45' 30" | 0
out diff_dms | Difference (DMS) | - | dms1 - dms2 | 0
out diff_dec | Difference (decimal degrees) | ° | dms1 - dms2 | 4