Degrees Minutes Seconds Calculator

Angle Calculator Form

Calculation type

Seconds precision

Main result range

Decimal degrees input

Used for decimal to DMS mode.

Angle A degrees

Angle A minutes

Angle A seconds

Angle A direction

Angle B degrees

Angle B minutes

Angle B seconds

Angle B direction

Example Data Table

Example	Input	Output	Use case
DMS to decimal	36° 15′ 30″ N	36.258333°	Survey point
Decimal to DMS	-74.005974°	-74° 0′ 21.5064″	Longitude record
Overflow DMS	120° 90′ 75″	121° 31′ 15″	Raw field notes
Add angles	5° 30′ 0″ + 2° 45′ 30″	8° 15′ 30″	Route bearing

Formula Used

DMS to decimal degrees:

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

South and west directions make the final value negative.

Decimal degrees to DMS:

Degrees = floor(abs(decimal))

Minutes = floor((abs(decimal) - degrees) × 60)

Seconds = remaining fraction × 3600

Radians:

Radians = Decimal Degrees × π / 180

Total arc seconds: Decimal Degrees × 3600

How to Use This Calculator

Select the calculation type from the first dropdown.
Enter decimal degrees when using decimal to DMS mode.
Enter Angle A DMS values for DMS conversion.
Enter Angle B values when adding or subtracting angles.
Choose a direction if your angle uses north, south, east, or west.
Select a normalization range when required.
Press calculate to see the result above the form.
Use CSV or PDF buttons to save the result.

Understanding Degree Minute Second Conversion

Angles are often stored in two popular formats. Decimal degrees are easy for software. Degrees, minutes, and seconds are easy for field notes. This calculator connects both formats. It also supports signed directions, angle addition, angle subtraction, and normalization.

Why DMS Still Matters

Surveyors, navigators, map editors, astronomers, and engineers still use DMS. The format breaks one degree into sixty minutes. Each minute has sixty seconds. This makes small angle changes readable. A decimal like 36.258333 becomes 36° 15′ 30″. The value is the same. Only the format changes.

Advanced Conversion Support

The tool accepts positive or negative degrees. It also reads north, south, east, and west direction choices. South and west create negative decimal values. Minutes and seconds can be larger than fifty nine. The calculator can normalize those values before showing the final result. This helps when raw notes contain overflow, such as 15° 75′ 80″.

Useful Angle Operations

Many projects need more than one conversion. You may add two DMS angles. You may subtract one angle from another. The page also reports radians, total arc minutes, and total arc seconds. These extra values help when angles must move into formulas, drawings, scripts, navigation tools, or technical reports.

Normalization Ranges

Angles may need a special range. A compass bearing usually fits 0° to 360°. A longitude style angle often fits -180° to 180°. This calculator provides both views. It also lets you choose which normalized value becomes the main answer. Keeping the raw result visible helps you audit the calculation.

Better Records And Exports

A clean result is useful only when it can be saved. Use the CSV option for spreadsheets. Use the PDF option for reports, estimates, and client notes. The example table shows common conversions and arithmetic cases. It can guide new users before they enter real data.

Accuracy Notes

Rounding controls the displayed seconds. More decimal places give a tighter DMS output. Less rounding gives a cleaner report. Use a precision that matches your source data. Old field notes rarely need excessive decimals. Digital mapping work may need more detail.

Always keep original notes beside the converted result safely.

FAQs

What does DMS mean?

DMS means degrees, minutes, and seconds. It is an angle format. One degree has sixty minutes. One minute has sixty seconds. It is often used in maps, surveying, navigation, and astronomy.

How do I convert DMS to decimal degrees?

Add degrees, minutes divided by sixty, and seconds divided by three thousand six hundred. Apply a negative sign for south or west directions.

Can this calculator handle negative angles?

Yes. You can enter negative degrees directly. You can also choose south or west direction. Those choices make the decimal result negative.

What happens when minutes exceed fifty nine?

The calculator accepts overflow values. For example, seventy five minutes becomes one degree and fifteen minutes. This helps clean raw field records.

What is the 0° to 360° range?

It is a normalized bearing range. Negative angles are wrapped into a positive full circle. This is useful for compass bearings and rotation work.

What is the -180° to 180° range?

This range keeps angles centered around zero. It is useful for longitude style values, shortest angular differences, and signed direction work.

Why is radians shown in the result?

Radians are common in math, programming, and engineering formulas. Showing radians saves another conversion step after the angle is calculated.

Can I export my calculation?

Yes. Use the CSV button for spreadsheet records. Use the PDF button for printable reports, client notes, and project files.