Adding Subtracting Degrees Minutes Seconds Calculator

How to Use This Calculator

Using our angle calculator is simple:

1. Enter the first angle in degrees, minutes, and seconds.
2. Enter the second angle in degrees, minutes, and seconds.
3. Select whether to add or subtract the angles.
4. Click "Calculate" to see the result.
5. Review the detailed breakdown of the calculation.

The calculator handles all the conversions between degrees, minutes, and seconds automatically, so you don't need to worry about manual unit conversions.

How Angle Addition/Subtraction Works

When adding or subtracting angles, you need to consider all components: degrees, minutes, and seconds. Here's how the calculation works:

The calculator performs these steps:

1. Converts all inputs to seconds for precise calculation
2. Performs the addition or subtraction
3. Converts the result back to degrees, minutes, and seconds
4. Handles overflow of seconds to minutes and minutes to degrees

Worked Examples

Example 1: Adding Angles

Let's add 45° 30' 15" and 22° 45' 30".

1. Convert both angles to seconds:
   • 45° 30' 15" = 45 × 3600 + 30 × 60 + 15 = 162,135 seconds
   • 22° 45' 30" = 22 × 3600 + 45 × 60 + 30 = 81,930 seconds
2. Add the seconds: 162,135 + 81,930 = 244,065 seconds
3. Convert back to degrees, minutes, seconds:
   • 244,065 ÷ 3600 = 67° with remainder 2,265 seconds
   • 2,265 ÷ 60 = 37' with remainder 45 seconds
   • Final result: 67° 37' 45"

Example 2: Subtracting Angles

Let's subtract 15° 20' 10" from 30° 15' 20".

1. Convert both angles to seconds:
   • 30° 15' 20" = 30 × 3600 + 15 × 60 + 20 = 108,920 seconds
   • 15° 20' 10" = 15 × 3600 + 20 × 60 + 10 = 55,210 seconds
2. Subtract the seconds: 108,920 - 55,210 = 53,710 seconds
3. Convert back to degrees, minutes, seconds:
   • 53,710 ÷ 3600 = 14° with remainder 3,310 seconds
   • 3,310 ÷ 60 = 55' with remainder 10 seconds
   • Final result: 14° 55' 10"