Worksheets · Precalculus

Precalculus degrees, minutes and seconds worksheet

A degree splits into 60 minutes and a minute into 60 seconds, so a second is 1/3600 of a degree. To go to decimal degrees, add the minutes over 60 and the seconds over 3600. To come back, multiply the decimal part by 60 for the minutes, and what is left by 60 again for the seconds.

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Pick more than one for a sheet that mixes them.

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Sigma Prep · sigmaprep.io/worksheets

Name

Degrees, Minutes and Seconds

Date Period

Convert each angle.

  1. Write in decimal degrees: 116∘ 59′ 15′′
  2. Write in degrees, minutes and seconds: 138.945∘
  3. Write in decimal degrees: 38∘ 19′ 39′′
  4. Write in degrees, minutes and seconds: 96.3875∘
  5. Write in decimal degrees: 35∘ 20′ 15′′
  6. Write in degrees, minutes and seconds: 101.6275∘
  7. Write in decimal degrees: 15∘ 52′ 39′′
  8. Write in degrees, minutes and seconds: 70.36∘
  9. Write in decimal degrees: 12∘ 48′ 9′′
  10. Write in degrees, minutes and seconds: 130.2925∘
  11. Write in decimal degrees: 167∘ 40′ 39′′
  12. Write in degrees, minutes and seconds: 145.6975∘
  13. Write in decimal degrees: 94∘ 11′ 42′′
  14. Write in degrees, minutes and seconds: 15.1125∘
  15. Write in decimal degrees: 116∘ 27′ 54′′
  16. Write in degrees, minutes and seconds: 179.815∘
  17. Write in decimal degrees: 82∘ 11′ 33′′
  18. Write in degrees, minutes and seconds: 101.3825∘
  19. Write in decimal degrees: 120∘ 2′ 24′′
  20. Write in degrees, minutes and seconds: 43.305∘

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Degrees, Minutes and SecondsAnswer keyVersion 1

Date Period

Convert each angle.

  1. Write in decimal degrees: 116∘ 59′ 15′′116.9875∘
  2. Write in degrees, minutes and seconds: 138.945∘138∘ 56′ 42′′
  3. Write in decimal degrees: 38∘ 19′ 39′′38.3275∘
  4. Write in degrees, minutes and seconds: 96.3875∘96∘ 23′ 15′′
  5. Write in decimal degrees: 35∘ 20′ 15′′35.3375∘
  6. Write in degrees, minutes and seconds: 101.6275∘101∘ 37′ 39′′
  7. Write in decimal degrees: 15∘ 52′ 39′′15.8775∘
  8. Write in degrees, minutes and seconds: 70.36∘70∘ 21′ 36′′
  9. Write in decimal degrees: 12∘ 48′ 9′′12.8025∘
  10. Write in degrees, minutes and seconds: 130.2925∘130∘ 17′ 33′′
  11. Write in decimal degrees: 167∘ 40′ 39′′167.6775∘
  12. Write in degrees, minutes and seconds: 145.6975∘145∘ 41′ 51′′
  13. Write in decimal degrees: 94∘ 11′ 42′′94.195∘
  14. Write in degrees, minutes and seconds: 15.1125∘15∘ 6′ 45′′
  15. Write in decimal degrees: 116∘ 27′ 54′′116.465∘
  16. Write in degrees, minutes and seconds: 179.815∘179∘ 48′ 54′′
  17. Write in decimal degrees: 82∘ 11′ 33′′82.1925∘
  18. Write in degrees, minutes and seconds: 101.3825∘101∘ 22′ 57′′
  19. Write in decimal degrees: 120∘ 2′ 24′′120.04∘
  20. Write in degrees, minutes and seconds: 43.305∘43∘ 18′ 18′′

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

34∘ 15′ 36′′ in decimal degrees

  1. 15 minutes is 15/60 = 0.25 of a degree.
  2. 36 seconds is 36/3600 = 0.01 of a degree.
  3. 34 + 0.25 + 0.01.

The answer is 34.26∘.

Where students go wrong

Treating the minutes as a decimal: 34 degrees 15 minutes is not 34.15 degrees. There are 60 minutes in a degree, not 100.

Also called degrees minutes seconds, DMS, decimal degrees or converting degrees to minutes and seconds.

What you can put on this worksheet

To decimal degrees
Write in decimal degrees: 48∘ 33′ → 48.55∘
To degrees, minutes and seconds
Write in degrees, minutes and seconds: 48.55∘ → 48∘ 33′

Questions about these worksheets

Yes. Every degrees, minutes and seconds sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the degrees, minutes and seconds questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: to decimal degrees and to degrees, minutes and seconds. Tick as many as you want and set how many of each, or let it spread them evenly.

Treating the minutes as a decimal: 34 degrees 15 minutes is not 34.15 degrees. There are 60 minutes in a degree, not 100.