Circle Calculator
Calculate a circle's area, circumference, and diameter from its radius.
How this calculator works
All three measurements derive from the radius using the constant π (pi).
r = radius
Real-world uses for circle calculations
Circle area and circumference calculations show up constantly in practical contexts — figuring out how much material covers a round table, how much fencing surrounds a circular garden, or how far a wheel travels per rotation (which relates directly to circumference).
For a wheel or circular object rolling without slipping, one full rotation covers a distance exactly equal to its circumference — a useful fact for calculating speed or distance from rotational measurements.
A worked example
A circle with radius 7: area equals pi times 7 squared, approximately 153.9 square units; circumference equals 2 times pi times 7, approximately 44.0 units; and diameter equals 14 units.
Doubling the radius to 14 doesn't just double the area — it quadruples it to roughly 615.8 square units, since area scales with the square of the radius, while circumference only doubles to about 88.0 units.
Where circle measurements matter in real life
Circle area and circumference calculations show up constantly in practical contexts — sizing a circular garden bed, calculating pipe cross-sections, determining wheel or tire measurements, or figuring out material needed for a round tabletop all rely on these same basic formulas.
For applied projects, it's worth double-checking whether you need radius or diameter, since mixing them up is one of the most common sources of calculation errors — remember diameter is always exactly twice the radius.
Frequently asked questions
What if I only know the diameter or circumference?
Divide the diameter by 2 to get the radius, or divide the circumference by 2π — then enter that radius value here.
How do I find the radius if I only know the area?
Divide the area by π, then take the square root of the result — r = √(Area ÷ π).
What's the value of π used in these calculations?
This calculator uses JavaScript's built-in π constant, accurate to about 15 decimal places — far more precision than needed for virtually any practical application.
What's the relationship between diameter and radius?
Diameter is always exactly twice the radius — if you know one, you can find the other by multiplying or dividing by 2.