Mini Minds Hub · Free printable
Circumference of a Circle: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Circumference of a Circle is a free printable maths worksheet for Year 7 (ages 11 to 12) in Key Stage 3. Children use the formula circumference = pi × diameter to find the distance round a circle. They also work backwards from a circumference to find a diameter or a radius. A calculator is fine, and page 2 gives the grown-up notes and answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to the child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
The sheet has eight questions. The first six give a diameter or a radius and ask children to find the circumference. The units change from question to question, so children must read each one with care. The last two go the other way. Each gives a circumference and asks for the diameter or the radius. There is space under each question for working and an answer.
- Diameter 10 cm. Find C
- Diameter 5 cm. Find C
- Diameter 20 m. Find C
- Radius 3 cm. Find C
- Radius 5 m. Find C
- Diameter 100 mm. Find C
- C = 31.4 cm. Find the diameter
- C = 62.8 cm. Find the radius
A worked example
A circle has a diameter of 8 cm. Find the circumference. Use pi = 3.14.
This is a different question from the ones on the sheet. It shows two ways to reach the same answer.
Method 1: use the diameter- Write the formula: C = pi × d.
- Put in the numbers: C = 3.14 × 8.
- Multiply: 3 × 8 = 24 and 0.14 × 8 = 1.12, so C = 25.12.
- The radius is half the diameter, so r = 4 cm.
- Use C = 2 × pi × r, which means double the radius, then multiply by pi.
- 2 × 3.14 × 4 = 6.28 × 4 = 25.12.
Building the idea
Start with a real circle
Hold a plate or a tin lid. Point to the distance across the middle and the distance all the way round. Ask which one is longer before any numbers appear.
Say the formula in words
Read C = pi × d as: the distance round is a little more than three times the distance across. This helps children spot a silly answer.
Estimate first
Before using the calculator, round pi to 3 and make a rough answer. Then compare it with the calculated one.
Write the units every time
The circumference is a length, so it uses the same unit as the diameter. Make this a habit on every line.
Circumference, diameter and pi
The circumference is the distance all the way round a circle. The diameter is the distance straight across, passing through the centre. The radius is the distance from the centre to the edge, so it is half the diameter. Many mistakes on circle questions come from mixing up the radius and the diameter, so it is worth checking which one a question gives.
Pi is the number you get when you divide the circumference of any circle by its diameter. It is the same for every circle, big or small. Its value is a little over 3, and 3.14 is a common approximation. The digits of pi never end and never repeat, so no decimal can write it exactly. The pi key on a calculator holds a much longer value.
Quick facts about circles and pi
- Every circle has the same value of pi, whatever its size.
- Pi is a little more than 3, so the distance round a circle is a little more than three diameters.
- The decimal digits of pi go on for ever without a repeating pattern.
- The diameter is always twice the radius.
- The symbol for pi is the Greek letter π.
Skills and curriculum link
- Using a formula
- Rearranging
- Working with decimals
- Radius and diameter
- Choosing units
- Checking answers
Ideas that help with this sheet
- PiPi links the distance round a circle to the distance across. Choose a value, such as 3.14 or the calculator key, and use it for every question.
- Radius to diameterIf a question gives the radius, double it to get the diameter. Do this step first and write it down.
- UnitsThe circumference has the same unit as the length you started with. Write the unit after every answer.
- Working backwardsIf multiplying by pi gives the circumference, then dividing the circumference by pi undoes it. Write the steps in order.
Key words
- CircumferenceThe distance all the way round the edge of a circle.
- DiameterA straight line across a circle through the centre.
- RadiusThe distance from the centre of a circle to its edge. It is half the diameter.
- PiThe number you get when you divide the circumference of a circle by its diameter. It is about 3.14.
- FormulaA rule written with letters or symbols that links quantities.
- RearrangeChange a formula around so a different quantity is on its own.
How to use it
- Print both pages. Page 1 is for the child. Keep page 2, which has the notes and answers.
- Agree which value of pi to use, such as 3.14 or the calculator key, and how to round.
- Do the first question together. Write the formula, then the numbers, then use the calculator.
- Let the child try the rest alone. Remind them to write the unit with each answer.
- Check with page 2 and ask how they got each answer. Come back another day to repeat the tricky ones.
Help, stretch and game ideas
If it feels too hard
Write the formula and the numbers before touching the calculator. Underline whether the question gives a radius or a diameter. If it is a radius, double it first. Try a rough estimate using 3 for pi to see if the answer is sensible.
To stretch confident children
Measure a round object with string, then lay the string along a ruler. Measure across the middle too. Divide the circumference by the diameter and check that the result is a little over 3. Try three objects and compare.
Make it a game
Find three round things at home, such as a plate, a mug and a tin. Estimate each circumference first, then measure with string. The closest estimate scores a point. Work out the diameters and see if the formula agrees.
Mistakes to watch for
Watch forA child uses the radius in place of the diameter.
Try thisUnderline the word in the question. If it says radius, double it before using the formula.
Watch forA child writes the wrong unit, or none at all.
Try thisMake the unit part of the answer line. The circumference uses the same unit as the length given.
Watch forWhen working backwards, a child multiplies by pi again.
Try thisAsk which operation undoes multiplying by pi. Then check by putting the answer back into the formula.
Talk about it
- How can you tell whether a question gives the radius or the diameter?
- Why is the circumference always a bit more than three times the diameter?
- What would you estimate before using the calculator?
- How do you work backwards from the circumference?
- Does the unit of your answer match the unit in the question? How do you know?
- Why can 3.14 only be an approximation for pi?
Take it off the page
String and ruler
Wrap string round a mug, then measure the string against a ruler. Measure across the top as well and compare the two lengths.
Wheel turn
Mark a spot on a bike tyre and roll the bike forward one full turn. Measure the distance travelled and compare it with the wheel's diameter.
Pi table
Draw a table with columns for object, circumference, diameter and circumference divided by diameter. Fill it in for four round things.
Who it is for
Parents
Sit with your child for the first question and let them explain each step. Do not worry about the calculator. Ask them to say how they know whether to double or divide.
Teachers
Use it as a starter, a plenary, an early finisher task, homework or a table activity. The mix of forward and backward questions suits mixed ability groups. Page 2 has help and stretch ideas.
Home educators
Pair it with real objects at home. Measuring round things with string makes the formula feel real. Keep the sheet to use again for revision or for brothers and sisters.
Where this fits in maths
Before this, children measure lengths and perimeters, multiply and divide decimals, and know the parts of a circle. Confidence with units and with using a calculator helps a lot here.
After this, children move on to the area of a circle and to perimeters of shapes that include parts of circles. Later still, they may leave answers in terms of pi. Rearranging formulae, practised here, is useful across Key Stage 3 maths and science.
Questions parents and teachers ask
- What age is Circumference of a Circle for?
It is written for Year 7 (ages 11 to 12) in Key Stage 3. It also suits older children who need revision on circles, and confident Year 6 children who are ready for a challenge.
- Can children use a calculator?
Yes. A calculator is fine. Children still need to write the formula and the numbers first, so the method is clear. Encourage a rough estimate before pressing any keys.
- Which value of pi should children use?
Use the value your class or teacher prefers, such as 3.14 or the pi key on a calculator. Agree this and the rounding before starting, so answers can be checked fairly.
- What if it feels too hard?
Start by writing the formula and the numbers before using the calculator. Check whether each question gives a radius or a diameter. Do the first few questions together, then try the rest another day.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or revision.
- Is this a screen free activity?
Yes. It needs only paper, a pencil and a calculator if you choose. It works well for quiet time, homework or a rainy day, and the string measuring idea gets children away from the page too.
- Can teachers and home educators use it?
Yes. Teachers can use it as a starter, plenary, early finisher task or homework. Home educators and tutors can use it alone or as part of a wider plan. It needs no preparation beyond printing.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.