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Adding Degrees Minutes and Seconds Calculator

Reviewed by Calculator Editorial Team

Adding degrees, minutes, and seconds (DMS) is a common task in navigation, astronomy, and surveying. This calculator provides a simple way to add two DMS values together, with clear instructions and examples to help you understand the process.

How to Add Degrees, Minutes, and Seconds

Adding DMS values involves converting each component to a common unit (seconds) and then performing the addition. Here's a step-by-step guide:

Step 1: Convert Degrees to Seconds

First, convert the degrees component of each DMS value to seconds. Since 1 degree = 3600 seconds:

Conversion Formula

Degrees to seconds = Degrees × 3600

Step 2: Convert Minutes to Seconds

Next, convert the minutes component of each DMS value to seconds. Since 1 minute = 60 seconds:

Conversion Formula

Minutes to seconds = Minutes × 60

Step 3: Add All Components

Add the converted degrees, minutes, and original seconds components together:

Addition Formula

Total seconds = (Degrees₁ × 3600) + (Minutes₁ × 60) + Seconds₁ + (Degrees₂ × 3600) + (Minutes₂ × 60) + Seconds₂

Step 4: Convert Back to DMS

Convert the total seconds back to degrees, minutes, and seconds:

  1. Divide the total seconds by 3600 to get degrees (integer part)
  2. Take the remainder and divide by 60 to get minutes (integer part)
  3. The remaining value is the seconds component

Formula Used

The complete formula for adding two DMS values is:

Complete Formula

Total DMS = (Degrees₁ + Degrees₂) + (Minutes₁ + Minutes₂) + (Seconds₁ + Seconds₂)

If any component exceeds its maximum value (60 for minutes/seconds), carry over to the next higher unit.

This formula assumes all inputs are valid DMS values where:

  • 0 ≤ Degrees < 360
  • 0 ≤ Minutes < 60
  • 0 ≤ Seconds < 60

Worked Examples

Example 1: Simple Addition

Add 10° 20' 30" and 5° 10' 15":

  1. Degrees: 10 + 5 = 15°
  2. Minutes: 20 + 10 = 30'
  3. Seconds: 30 + 15 = 45"

Result: 15° 30' 45"

Example 2: With Carry Over

Add 10° 59' 50" and 0° 1' 20":

  1. Degrees: 10 + 0 = 10°
  2. Minutes: 59 + 1 = 60' → 1° 0'
  3. Seconds: 50 + 20 = 70" → 1' 10"
  4. Combine: 10° + 1° = 11°; 0' + 1' = 1'; 10" + 0" = 10"

Result: 11° 1' 10"

Frequently Asked Questions

How do I add degrees, minutes, and seconds?

To add DMS values, simply add the degrees, minutes, and seconds components separately. If any component exceeds its maximum value (60 for minutes/seconds), carry over to the next higher unit.

What if I have more than two DMS values to add?

You can add multiple DMS values by adding them sequentially. For example, to add A, B, and C, first add A and B, then add the result to C.

Can I subtract DMS values with this calculator?

No, this calculator is specifically designed for adding DMS values. For subtraction, you would need to convert to seconds, subtract, and then convert back to DMS.

What if my DMS values are negative?

This calculator works with positive DMS values only. For negative values, you would need to handle the signs separately according to your specific use case.