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Add Degrees Minutes and Seconds Calculator

Reviewed by Calculator Editorial Team

This calculator adds together degrees, minutes, and seconds to produce a single combined angle measurement. It's useful for astronomers, surveyors, and anyone working with angular measurements in navigation, construction, or science.

How to Use This Calculator

To add degrees, minutes, and seconds:

  1. Enter the degrees value in the first field
  2. Enter the minutes value in the second field (0-59)
  3. Enter the seconds value in the third field (0-59)
  4. Repeat for the second angle you want to add
  5. Click "Calculate" to see the combined result

The calculator will automatically handle overflow from seconds to minutes and minutes to degrees, ensuring accurate results.

Formula Explained

Conversion Formula

First, convert all measurements to decimal degrees:

Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600)

Then add the two decimal degree values together.

Finally, convert the sum back to degrees, minutes, and seconds if needed.

This method ensures precise calculations while maintaining the standard angular measurement format.

Worked Examples

Example 1: Simple Addition

Add 10° 20' 30" and 5° 10' 15":

  1. Convert first angle: 10 + (20/60) + (30/3600) = 10.3417°
  2. Convert second angle: 5 + (10/60) + (15/3600) = 5.1708°
  3. Add: 10.3417° + 5.1708° = 15.5125°
  4. Convert back: 15° + (0.5125 × 60) = 15° 30' 45"

Example 2: With Overflow

Add 10° 59' 50" and 0° 1' 10":

  1. Convert first angle: 10 + (59/60) + (50/3600) ≈ 10.9972°
  2. Convert second angle: 0 + (1/60) + (10/3600) ≈ 0.0208°
  3. Add: 10.9972° + 0.0208° = 11.0180°
  4. Convert back: 11° + (0.0180 × 60) ≈ 11° 1' 5"

Frequently Asked Questions

What is the difference between degrees, minutes, and seconds?

Degrees measure large angles, minutes measure smaller divisions (1° = 60'), and seconds measure even smaller divisions (1' = 60"). This system allows precise angular measurements.

Can I add more than two angles at once?

This calculator is designed for adding two angles at a time. For more complex calculations, you may need to add them sequentially.

How does the calculator handle negative angles?

The calculator works with positive angles only. For subtraction, you would need to use a separate calculator or manually convert to decimal degrees.

Is this calculator accurate for all applications?

Yes, the calculator uses standard conversion formulas and handles overflow between units automatically for precise results.