Worksheets · Precalculus

Degrees, minutes and seconds worksheet for Precalculus

Precalculus works with angles in several forms, and degrees, minutes and seconds is the one used for latitude, surveying and navigation. You convert in both directions, working in base 60 instead of base 10 and rounding seconds to the nearest whole number.

Also taught in Algebra 2, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Degrees, Minutes and Seconds

Date Period

Convert each angle.

  1. Convert to decimal degrees

    Write in decimal degrees: 134∘ 37′ 30′′
  2. Write in decimal degrees: 165∘ 50′ 33′′
  3. Write in decimal degrees: 17∘ 19′ 48′′
  4. Write in decimal degrees: 123∘ 59′ 33′′
  5. Write in decimal degrees: 50∘ 6′ 36′′
  6. Write in decimal degrees: 118∘ 31′ 3′′
  7. Write in decimal degrees: 22∘ 54′ 9′′
  8. Write in decimal degrees: 50∘ 42′ 9′′
  9. Write in decimal degrees: 146∘ 37′ 3′′
  10. Write in decimal degrees: 96∘ 26′ 33′′

  1. Convert from decimal degrees

    Write in degrees, minutes and seconds: 70.9675∘
  2. Write in degrees, minutes and seconds: 21.355∘
  3. Write in degrees, minutes and seconds: 93.04∘
  4. Write in degrees, minutes and seconds: 119.4225∘
  5. Write in degrees, minutes and seconds: 161.675∘
  6. Write in degrees, minutes and seconds: 87.0975∘
  7. Write in degrees, minutes and seconds: 31.9775∘
  8. Write in degrees, minutes and seconds: 150.205∘
  9. Write in degrees, minutes and seconds: 142.1575∘
  10. Write in degrees, minutes and seconds: 18.9325∘

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

Sigma Prep · sigmaprep.io/worksheets

Name

Degrees, Minutes and SecondsAnswer keyVersion 2

Date Period

Convert each angle.

  1. Convert to decimal degrees

    Write in decimal degrees: 134∘ 37′ 30′′134.625∘
  2. Write in decimal degrees: 165∘ 50′ 33′′165.8425∘
  3. Write in decimal degrees: 17∘ 19′ 48′′17.33∘
  4. Write in decimal degrees: 123∘ 59′ 33′′123.9925∘
  5. Write in decimal degrees: 50∘ 6′ 36′′50.11∘
  6. Write in decimal degrees: 118∘ 31′ 3′′118.5175∘
  7. Write in decimal degrees: 22∘ 54′ 9′′22.9025∘
  8. Write in decimal degrees: 50∘ 42′ 9′′50.7025∘
  9. Write in decimal degrees: 146∘ 37′ 3′′146.6175∘
  10. Write in decimal degrees: 96∘ 26′ 33′′96.4425∘

  1. Convert from decimal degrees

    Write in degrees, minutes and seconds: 70.9675∘70∘ 58′ 3′′
  2. Write in degrees, minutes and seconds: 21.355∘21∘ 21′ 18′′
  3. Write in degrees, minutes and seconds: 93.04∘93∘ 2′ 24′′
  4. Write in degrees, minutes and seconds: 119.4225∘119∘ 25′ 21′′
  5. Write in degrees, minutes and seconds: 161.675∘161∘ 40′ 30′′
  6. Write in degrees, minutes and seconds: 87.0975∘87∘ 5′ 51′′
  7. Write in degrees, minutes and seconds: 31.9775∘31∘ 58′ 39′′
  8. Write in degrees, minutes and seconds: 150.205∘150∘ 12′ 18′′
  9. Write in degrees, minutes and seconds: 142.1575∘142∘ 9′ 27′′
  10. Write in degrees, minutes and seconds: 18.9325∘18∘ 55′ 57′′

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

How to do these

Write 47.3825∘ in degrees, minutes and seconds

  1. Keep the 47 degrees. Then 0.3825 × 60 = 22.95, so 22 minutes.
  2. The leftover 0.95 minutes × 60 = 57 seconds.

The answer is 47∘ 22′ 57′′.

Where students go wrong

Multiplying the whole angle by 60 instead of only the decimal part. In 47.3825°, only 0.3825 becomes minutes; the 47 degrees stay as they are.

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 and minutes: 48.55∘ → 48∘ 33′
Negative angles both ways
Convert to decimal degrees: −196∘ 42′ 0′′ → −196.7∘

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 3: to decimal degrees, to degrees, minutes and seconds and negative angles both ways. 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.