Introduction

A single angle can be written as a plain decimal number, or split into whole degrees, minutes and seconds. The Degrees Minutes Seconds Calculator takes whichever form you have and instantly shows the other, so you never have to do the base-60 arithmetic by hand.

The two angle boxes always hold the same value, just written differently:

Decimal degrees: one number, for example $33.8688$ .
DMS — degrees, minutes and seconds: for example $33^{\circ}\,52'\,7.68"$ .

Surveyors, navigators, astronomers, machinists and students all run into DMS on printed maps, charts, instruments and field notes. This calculator also converts to and from radians, gradians, turns and related angle units, so you can read any of them in a form your next tool expects.

How to use / quick start

1Type the angle you already have into either box. Use the Angle in degrees minutes seconds field (three sub-boxes for degrees, minutes and seconds) for a value like $33^{\circ}\,52'\,7.68"$ , or the Angle in degree field for a decimal value like $33.8688$ .
2If the angle is in another unit, switch the unit menu on either field — radians, gradians (gon), turns, $\pi$ radians, arcminutes, arcseconds, milliradians or microradians. Both boxes keep showing the same angle in your chosen units.
3The other box updates automatically as you type. Read the converted value and copy whichever form your spreadsheet, map, chart or program expects.

Worked example — $33^{\circ}\,52'\,7.68"$ in decimal degrees

Type $33$ , $52$ and $7.68$ into the three DMS sub-boxes. The calculator adds the degrees, the minutes divided by 60, and the seconds divided by 3600:

\mathrm{DD} = 33 + \frac{52}{60} + \frac{7.68}{3600}

=

33 + 0.8667 + 0.0021

=

33.8688^{\circ}

So $33^{\circ}\,52'\,7.68" = 33.8688^{\circ}$ . Type the decimal value the other way round and the DMS box fills in with the same angle split into whole degrees, minutes and seconds.

Because both fields are editable and the conversion runs both ways, you can correct any single value and the other field follows — you never have to re-enter the whole angle.

Real-world examples

Land survey: a DMS bearing into a spreadsheet

A surveyor reads a bearing of $47^{\circ}\,23'\,31.2"$ off a theodolite and needs the decimal value for a spreadsheet or GIS field. Type the three parts into the DMS field and read the decimal degrees:

\mathrm{DD} = 47 + \frac{23}{60} + \frac{31.2}{3600}

=

47 + 0.3833 + 0.0087

=

47.392^{\circ}

The result is $47.392^{\circ}$ , ready to paste wherever a single decimal number is expected.

Chart labeling: a decimal angle into DMS

A spreadsheet holds an angle of $48.8584^{\circ}$ and the printed chart needs it in degrees, minutes and seconds. Type the decimal value into the degree field and read the split:

M = 0.8584 \times 60

=

51.504

S = 0.504 \times 60

=

30.24

So $48.8584^{\circ} = 48^{\circ}\,51'\,30.24"$ — the whole degrees come from the integer part, and the leftover fraction is split into minutes and seconds.

Calculation method

The whole system rests on one rule: there are $60$ minutes in a degree and $60$ seconds in a minute, so a degree contains $3600$ seconds.

From DMS to decimal degrees

Each minute contributes a sixtieth of a degree and each second a 3600th, so the decimal value is:

\mathrm{DD} = D + \frac{M}{60} + \frac{S}{3600}

The reverse direction takes the decimal value apart: the whole degrees come from the integer part of the absolute value, the minutes are the leftover fraction multiplied by $60$ , and the seconds are what remains after that:

D = \lfloor |\mathrm{DD}| \rfloor

M = \lfloor (|\mathrm{DD}| - D) \cdot 60 \rfloor

S = ((|\mathrm{DD}| - D) \cdot 60 - M) \cdot 60

The floor step is what keeps minutes and seconds whole: the decimal value is broken at the whole minutes boundary, and the leftover fraction becomes the seconds.

Other angle units

The same angle can be written in radians, gradians, turns and the rest. The key reference points are:

360^{\circ} = 2\pi\ \mathrm{rad} = 400\ \mathrm{gon} = 1\ \mathrm{turn}

A radian is roughly $57.2958^{\circ}$ , a gradian is $0.9^{\circ}$ , and the $\times\ \pi\ \mathrm{rad}$ unit counts in multiples of $\pi$ , so $1$ there means $180^{\circ}$ . Switch the unit menu on either field and both boxes re-read the same angle in the new unit.

For a negative angle, the minus sign lives on the degrees field and the minutes and seconds stay positive — that matches how DMS is normally written. The calculator also carries overflow for you: because $60'' = 1'$ and $60' = 1^{\circ}$ , entering $5^{\circ}\,75'\,30"$ reads back as $6^{\circ}\,15'\,30"$ .

Tips & best practices

Put the sign on the degrees, not the minutes
For a negative angle, type the minus sign on the degree field only — minutes and seconds are always treated as positive magnitudes. A value written $-33^{\circ}\,52'\,7.68"$ is entered as $-33$ , $52$ and $7.68$ in the three DMS boxes.
Don't mix degrees with radians
Confusing radians and degrees is one of the most common angle errors. If a result that should be around $30^{\circ}$ comes out near $0.52$ , the source value was almost certainly radians — switch that field to radians and re-check the reading.
Understand the carry at 60
Because $60'' = 1'$ and $60' = 1^{\circ}$ , an entry like $44^{\circ}\,59'\,60"$ is the same angle as $45^{\circ}$ , and the calculator will show it that way. Keeping minutes and seconds under 60 makes your input easier to check.
Think in the size of a second
One second of arc is only $\frac{1}{3600}$ of a degree, about $0.000278^{\circ}$ . If your source gives decimal degrees with only one or two decimals, the converted seconds will look unstable even though the angle itself is correct — add more decimal places to the input for a steadier DMS reading.

Related concepts

Why 60 minutes and 60 seconds?

The habit of splitting a degree into 60 minutes and a minute into 60 seconds goes back to the ancient Babylonian base-60 (sexagesimal) number system. It stuck because it is still convenient for navigation, astronomy, surveying and timekeeping — angles and time share the same subdivision:

1^{\circ}

=

60'

=

3600''

The same base-60 pattern drives time: just as $1\ \mathrm{hour} = 60\ \mathrm{minutes}$ , a degree is split into $60$ minutes of arc and each minute into $60$ seconds — which is why time and angles feel so natural side by side.

Degrees, radians, gradians and turns

Degrees are the everyday and geographic choice, radians are the standard in mathematics and physics, gradians appear in some surveying and engineering work, and turns are used when a full rotation is the natural unit. They all describe the same amount of rotation:

360^{\circ}

=

2\pi\ \mathrm{rad}

=

400\ \mathrm{gon}

=

1\ \mathrm{turn}

The calculator accepts all of these — plus $\pi$ radians, arcminutes, arcseconds, milliradians and microradians — on either field, so you can read the same angle in whatever unit your next tool wants.

Coordinates are angles too

Latitude and longitude are just angles measured from the equator and the Greenwich meridian, and they are often recorded in DMS — for example $33^{\circ}\,52'\,7.68"\,S$ . This calculator converts any single angle, including those coordinate-style values.

If you are working with full coordinate pairs — including N/S/E/W directions and the degrees-decimal-minutes format — the Coordinates Converter handles latitude and longitude directly in all three formats.

Why this matters

DMS is the format you read on paper — printed maps, charts, field notes and instruments — while decimal degrees is what most software, spreadsheets and databases expect. A reliable converter moves between them without transcription slips, so the angle on your paper notes and the number in your system stay exactly the same.

Frequently asked questions

Can I use this to convert latitude and longitude?

Yes for the angle itself — a DMS latitude or longitude is converted here exactly like any other angle. But for coordinate pairs with N/S/E/W direction letters and the degrees-decimal-minutes format, the Coordinates Converter is built for that job and shows both axes together.

How do I enter a negative angle?

Type the minus sign on the degree field only. Minutes and seconds are always entered as positive numbers — for example $-33^{\circ}\,52'\,7.68"$ is entered as $-33$ , $52$ and $7.68$ .

Why did $44^{\circ}\,59'\,60"$ come back as $45^{\circ}\,0'\,0"$ ?

Because the angle is carried at 60, the same rule as time: $60" = 1'$ and $60' = 1^{\circ}$ . The calculator normalizes any overflow, so $44^{\circ}\,59'\,60"$ is mathematically the same angle as $45^{\circ}$ and is shown that way.

Limitations

This calculator changes how an angle is written — it does not measure angles or add accuracy beyond the numbers you type. The result is only as precise as the input.
Negative angles and angles beyond a full turn are kept exactly as typed. If your application expects a bearing in a fixed $0^{\circ}$ – $360^{\circ}$ range, you may need to normalize the value yourself.
In formal surveying, navigation or legal boundary work, always confirm the notation, datum and source of an angle with a qualified professional before relying on it.

Degrees Minutes Seconds Calculator

Introduction

How to use / quick start

Real-world examples

Land survey: a DMS bearing into a spreadsheet

Chart labeling: a decimal angle into DMS

Calculation method

Tips & best practices

Frequently asked questions

Can I use this to convert latitude and longitude?

How do I enter a negative angle?

Why did $44^{\circ}\,59'\,60"$ come back as $45^{\circ}\,0'\,0"$ ?

Limitations

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Introduction

How to use / quick start

Real-world examples

Land survey: a DMS bearing into a spreadsheet

Chart labeling: a decimal angle into DMS

Calculation method

Tips & best practices

Related concepts

Why 60 minutes and 60 seconds?

Degrees, radians, gradians and turns

Coordinates are angles too

Why this matters

Frequently asked questions

Can I use this to convert latitude and longitude?

How do I enter a negative angle?

Why did 44∘ 59′ 60"44^{\circ}\,59'\,60"44∘59′60" come back as 45∘ 0′ 0"45^{\circ}\,0'\,0"45∘0′0"?

Limitations

Related Calculators

Scale Calculator

Trajectory Calculator

Projectile Range Calculator

Projectile Motion Calculator

Maximum Height Calculator – Projectile Motion

Time of Flight Calculator – Projectile Motion

Why did $44^{\circ}\,59'\,60"$ come back as $45^{\circ}\,0'\,0"$ ?