## Video Lesson: How to Convert Degrees to Degrees, Minutes and Seconds to Decimal Degrees

## What are Degrees, Minutes and Seconds?

**Degrees, Minutes and Seconds are precise measurements of angles used to describe longitude and latitude. There are 360 degrees in a full circle. Each degree is divided into 60 minutes and each minute is divided further into 60 seconds. **

Degrees, minutes and seconds (DMS) are used in describing location using longitudinal and latitudinal coordinates. Since the earth is so large, very accurate units are required to measure specific locations. Two positions of measurement will be required to obtain a location. That is the angle of longitude (east or west) and the angle of latitude (north or south).

- The symbol for degrees is a small circle °.
- The symbol for minutes is an apostrophe ‘.
- The symbol for seconds is two apostrophes ”.

For example, 3 degrees, 16 minutes and 7 seconds is written as 3° 16′ 7”.

### What is a Degree in Angle Measurement?

**A degree** **is a measurement of an angle that is equal to 1/360th of a full turn. The symbol for degrees is °**.

**There are 90 degrees in a right angle, 180 degrees in a straight line and 360 degrees in a full turn.**

### What is a Minute in Angle Measurment?

**A minute is an angle the size of 1/60th of a degree. There are 60 minutes in 1 degree. ****The symbol for minutes is a dash (‘). For example, 2 and a half degrees is equivalent to 2 degrees and 30 minutes, written as 2***°* 30′.**There are 21600 minutes in a full turn. **

### What is a Second in Angle Measurement?

**A full turn is divided into 360 degrees. These degrees are divided further into 60 minutes and each minute can be divided into 60 seconds. A second is an angle the size of 1/3600th of a degree. There are 3600 seconds in one degree and 1 296 000 seconds in a full turn. **

## How to Convert Decimal Degrees to Degrees, Minutes and Seconds

**To convert decimal degrees to degrees, minutes and seconds:**

- Subtract the whole number, which is the amount of degrees.
- Multiply the remaining decimal by 60.
- Subtract the whole number from this result which is the amount of minutes.
- Multiply the remaining decimal by 60.
- Subtract the whole number from this result which is the amount of seconds.

For example, convert 14.5° to degrees, minutes and seconds.

**Step 1. Subtract the whole number, which is the amount of degrees**

** **The degrees are shown before the decimal point. Therefore, the number of degrees is simply 14.

Subtracting the whole number: 14.5 – 14 = 0.5.

We still have 0.5 of a degree to convert into minutes and seconds.

**Step 2. Multiply the remaining decimal by 60**

0.5 × 60 = 30.

**Step 3. Subtract the whole number from this result, which is the amount of minutes.**

The whole number is 30 and so, there are 30 minutes.

In this example, there are no further decimals and so, we have completed the conversion.

14.5° is 14 degrees and 30 minutes.

There are no seconds.

**To convert 23.14° to degrees, minutes and seconds:**

- Subtract the whole number, which is the degrees (23°).
- Multiply the remaining decimal by 60 (0.14 × 60 = 8.4).
- Subtract the whole number, which is the minutes (8′).
- Multiply the remaining decimal by 60 (0.4 × 60 = 24).
- Subtract the whole number, which is the seconds (24”).

The number before the decimal point is simply the number of degrees. So we have 24°.

The decimal part is multiplied by 60 to obtain the amount of minutes. So we have 8.4 minutes. We write 8′.

We multiply the decimal part by 60 to obtain the amount of seconds. So we have 24 seconds. We write 24”.

## How to Convert Degrees, Minutes and Seconds to Decimal Degrees

**To convert degrees, minutes and seconds to decimal degrees, add the number of degrees to the number of minutes divided by 60 to the number of seconds divided by 3600.**

Formula for converting degrees, minutes and seconds to decimal degrees

For example, convert 12° 30′ 36” to decimal degrees.

The number of degrees is 12.

The number of minutes is 30.

The number of seconds is 36.

Using the formula, :

This becomes .

The final answer is 12.51°

Here is an example of converting degrees, minutes and seconds to decimal degrees in steps.

**To convert degrees, minutes and seconds to decimal degrees in steps:**

- Divide the number of minutes by 60 to convert them to degrees.
- Divide the number of seconds by 3600 to convert them to degrees.
- Add these two results to the number of degrees given.

Convert 67 degrees 15 minutes and 54 seconds into decimal degrees.

**Step 1. Divide the number of minutes by 60 to convert them to degrees**

We have 15 minutes.

15 ÷ 60 = 0.25.

We have converted 15 minutes to 0.25 degrees.

**Step 2. Divide the number of seconds by 3600 to convert them to degrees**

We have 54 seconds.

54 ÷ 3600 = 0.015.

We have converted 54 seconds to 0.015 degrees.

**Step 3. Add these two results to the number of degrees given**

In this example of 67° 15′ 54”, we have 67 degrees.

We add this to the two results obtained in steps 1 and 2.

64 + 0.25 + 0.015 = 67.265°.

## How to Convert to Degrees, Minutes and Seconds on a Calculator

**On a calculator, enter the number of decimal degrees and press [=]. Then press the [° ‘ “] button to convert to degrees, minutes and seconds.**

Here is the button shown on a Casio calculator.

## How to Convert Degrees, Minutes and Seconds to Degrees on a Calculator

**To convert degrees, minutes and seconds to degrees on a calculator, type the number of degrees, press [° ‘ “], type the number of minutes, press [° ‘ “], type the number of seconds, press [° ‘ “] and finally press [=].**

This is shown on the Casio calculator below.