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Adding Degrees Minutes Seconds Calculator

Reviewed by Calculator Editorial Team

This calculator helps you add angles measured in degrees, minutes, and seconds. Whether you're working with geographic coordinates, astronomy, or engineering measurements, this tool provides precise results by properly converting and combining all components.

How to Use This Calculator

To add two angles measured in degrees, minutes, and seconds:

  1. Enter the first angle in the "First Angle" section
  2. Enter the second angle in the "Second Angle" section
  3. Click "Calculate" to see the sum
  4. The result will appear in the same format (degrees, minutes, seconds)

The calculator automatically handles overflow between minutes and seconds, and between degrees and minutes, ensuring accurate results.

Formula Used

To add two angles (D°M' S") + (D°M' S"):

  1. Add the seconds: S₁ + S₂
  2. If the sum ≥ 60, add 1 to minutes and subtract 60 from seconds
  3. Add the minutes: M₁ + M₂ + carry from seconds
  4. If the sum ≥ 60, add 1 to degrees and subtract 60 from minutes
  5. Add the degrees: D₁ + D₂ + carry from minutes

This process ensures all components remain within their valid ranges (0-59 for minutes and seconds, 0-359 for degrees).

Worked Example

Let's add 45°30'15" and 22°45'50":

  1. Add seconds: 15 + 50 = 65 → 1 minute carryover, 5 seconds
  2. Add minutes: 30 + 45 + 1 = 76 → 1 degree carryover, 16 minutes
  3. Add degrees: 45 + 22 + 1 = 68
  4. Final result: 68°16'5"

This matches what our calculator would produce.

FAQ

What if I enter more than 59 minutes or seconds?

The calculator automatically converts excess minutes to degrees and excess seconds to minutes, so you don't need to pre-convert your values.

Can I add more than two angles at once?

Currently the calculator adds two angles at a time. For multiple angles, you would need to add them sequentially.

What's the maximum angle I can enter?

The calculator can handle angles up to 359°59'59" before rolling over to 0°.