Circle Geometry Question Generator
Two formulae, one radius, and one step that trips people up more than either formula: when the diameter is given instead of the radius, it has to be halved first. Squaring the diameter by mistake gives exactly four times the right area, which is a distinctive enough error that it is worth practising the halving deliberately. Questions here mix radius and diameter, and mix area with circumference.
What this generator does
Produces circle questions asking for either the area or the circumference, given either the radius or the diameter. Answers are to two decimal places, since both formulae involve π and neither gives a whole number for a whole radius.
How to use this tool
- Choose how many circles you want and at what level.
- Check whether you have been given the radius or the diameter.
- Apply the right formula and give the answer to two decimal places.
- Reveal the working to see the halving step written out where it applies.
Understanding the controls
- How many questions
- Between 1 and 20. Fifteen is comfortable because each question is short.
- Level
- Gentle always gives the radius and keeps it under ten. Standard and stretch sometimes give the diameter instead, and widen the range.
- Seed
- Reproduces the same circles from the same word.
- Show the answers / working
- The value, or the formula, the halving step where it applies and the substitution.
Common use cases
- Practice at spotting whether a radius or a diameter has been given
- Mixing area and circumference so the formulae are chosen rather than repeated
- Showing why a diameter mistake multiplies the area by four
- Getting used to answers that carry π and therefore need rounding
- Generating a repeatable set of circle questions for a class
How this generator works
A radius is drawn and the question presents either it or its double. The area is πr² and the circumference 2πr, both rounded to two places. The check recomputes from the stored radius and requires the rounded values to match, so a question that has been given the wrong formula cannot be shown.
Randomness and fairness
The radius, and whether the question gives the radius or the diameter, are random. The formulae are not. Seeded sets are reproducible and therefore explicitly not cryptographically secure; unseeded ones draw from the browser's cryptographically secure generator.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Only whole circles. Sectors, arcs and segments are not among the question types.
- Answers are decimal rather than left in terms of π, which some syllabuses prefer.
- Lengths are always in centimetres, so unit conversion is not exercised.
- No diagram is drawn.
- No circle you generate is kept; seed the set to get it back.
Privacy and your data
Circles and answers are generated in your browser and never transmitted. Nothing persists after you close the page.
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