Math
Circle Calculator
Give this circle calculator any one measurement — radius, diameter, circumference, or area — and it solves the other three, keeping answers exact in terms of π (like 36π) alongside decimals.
Add a central angle to get the arc length, sector area, chord, and segment for that slice.
Every circle measurement can be turned back into the radius, so one value is enough.
Enter the measurement in the unit you pick below. Area is in square units.
Lengths use this unit; area uses the square of it.
Optional. The slice angle used for arc length, sector area, chord, and segment. 90° is a quarter circle.
Try an example
Result
Area
—
- Radius
- —
- Diameter
- —
- Circumference
- —
- Arc length
- —
- Sector area
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the circle calculator solves
Every circle is fully described by its radius. The diameter is twice the radius, the circumference is 2π times the radius, and the area is π times the radius squared. That means one known value pins down all the others: the calculator converts whatever you enter back into the radius, then rebuilds the rest.
Reverse formulas (solving for the radius)
| You know | Radius formula | Example |
|---|---|---|
| Diameter d | r = d / 2 | d = 10 → r = 5 |
| Circumference C | r = C / (2π) | C = 12π → r = 6 |
| Area A | r = sqrt(A / π) | A = 36π → r = 6 |
Exact answers in terms of π
When the radius is a whole number or simple fraction, the circumference and area are exact multiples of π. Teachers often ask for that The answer kept as a fraction or radical instead of a rounded decimal.: a radius of 6 gives circumference 12π and area 36π. The calculator shows the exact form first and the decimal (using π ≈ 3.14159265) beside it. If you start from a rounded circumference or area, the radius is no longer a nice number, so only decimals are shown.
Sector, arc, chord, and segment
A central angle θ cuts the circle into a slice (sector). The arc is the curved edge of that slice, the chord is the straight line joining the arc's ends, and the segment is the region between the chord and the arc.
How to use it
- Choose which measurement you already have: radius, diameter, circumference, or area.
- Type its value and pick a unit (leave it on generic units for homework).
- Optionally change the central angle to get the sector and arc for a specific slice.
- Read the exact form (with π) when your teacher asks for it, or the decimal when you need a measurement.
How to read the answer
- Radius, diameter, circumference, and arc length are lengths and use the linear unit (cm, in, ...).
- Area, sector area, and segment area are areas and use square units (cm², in², ...).
- Circumference in π form: 12π means 12 × 3.14159... ≈ 37.6991.
- Doubling the radius doubles the circumference but multiplies the area by 4.
Common mistakes and edge cases
- Mixing up radius and diameter: the diameter is the full width through the center; the radius is half of it.
- Squaring the diameter instead of the radius in A = πr²: with d = 10, the area is π(5)² = 25π, not 100π.
- Using square units for circumference or plain units for area — the calculator labels each result so you can copy the right one.
- A radius of 0 or a negative value cannot form a circle, so the calculator returns an error instead of a fake answer.
- Angles above 360° do not describe a single slice; the sector helper falls back to 90° and warns you.
Worked examples
Radius 6 (classic exact answer)
r = 6 gives circumference 12π and area 36π.
Area
113.0973
Diameter 10 cm
Radius 5 cm, area 25π cm².
Area
78.5398
Circumference 31.4159 in
Working backward from a measured circumference (radius ≈ 5 in).
Area
78.5397
Area 50 square units
Radius = sqrt(50/π) ≈ 3.9894; circumference ≈ 25.0663.
Area
50
Decimal radius 2.5 m
Area = 6.25π m² (19.635 m²).
Area
19.635
Zero radius (impossible)
A circle with radius 0 has no size.
Area
—
Frequently asked questions
What is the formula for the area of a circle?+
A = πr², where r is the radius. If you only know the diameter, use r = d/2 first, or the equivalent form A = πd²/4.
How do I find the circumference from the area?+
Solve the area formula for the radius, r = sqrt(A/π), then use C = 2πr. Combined: C = 2·sqrt(πA). For A = 36π that gives C = 12π.
What does 36π mean as an answer?+
It is the exact area written as a multiple of π. Multiply by 3.14159... to get the decimal 113.097. Exact forms avoid rounding and are what most teachers want on tests.
Is the diameter the same as the radius?+
No. The diameter goes all the way across the circle through the center and is twice the radius. A circle with diameter 10 has radius 5.
Which value of π does the calculator use?+
It uses full double-precision π (3.141592653589793) for the decimal results and shows the exact multiple of π separately, so nothing is rounded early.
How do I find the area of a sector?+
A sector with central angle θ (in degrees) covers θ/360 of the circle, so its area is (θ/360)·πr². A 90° sector of a radius-6 circle has area 9π.
Why does doubling the radius quadruple the area?+
Area depends on r squared. Doubling r makes r² four times as large, so the area is four times as large, while the circumference (which depends on r, not r²) only doubles.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026