Given radius
Input: r = 7 cm
Substitution: C = 2π(7), A = π(7²)
Exact: C = 14π cm, A = 49π cm²
Rounded: C ≈ 43.98 cm, A ≈ 153.94 cm²
Circle Calculator: Area, Circumference, Diameter & Radius
Solve a Circle
Decimal places control display rounding. Consistency checks allow small differences caused by rounding.
Results
The diagram updates after calculation and uses your selected output units.
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Worked Examples
Given diameter
Input: d = 10 in
Substitution: r = 10/2, A = π(5²)
Exact: C = 10π in, A = 25π in²
Rounded: C ≈ 31.42 in, A ≈ 78.54 in²
Given circumference
Input: C = 18 m
Substitution: r = 18/(2π), A = 18²/(4π)
Exact: r = 9/π m, A = 81/π m²
Rounded: r ≈ 2.86 m, A ≈ 25.78 m²
Given area
Input: A = 64 ft²
Substitution: r = √(64/π), d = 2√(64/π)
Exact: r = 8/√π ft, C = 16√π ft
Rounded: r ≈ 4.51 ft, C ≈ 28.36 ft
How the Circle Calculator Works
A circle is one of the simplest and most useful shapes in mathematics. It is the set of all points in a plane that are the same distance from a central point. That distance is the radius r. From the radius we can find the diameter d = 2r, the circumference (the perimeter of the circle) C = 2πr, and the area (the size of the disk) A = πr². Because all four quantities are linked, knowing any one of them lets this calculator determine the others.
To maximize accuracy and learning value, the tool follows a consistent process: (1) it interprets your inputs and prefers to infer the radius first; (2) it derives the remaining measures from that radius; (3) if you provide more than one value, the calculator checks whether they are consistent within a small numerical tolerance and flags mismatches. You can also choose how many decimal places to display and which approximation of π to use—either the native high-precision value from your browser or familiar classroom approximations like 22/7 or 3.14. This makes the tool suitable for both quick homework checks and more precise engineering-style calculations.
Here’s what each quantity represents and how it’s used:
- Diameter: the full width across the circle through its center;
d = 2r. - Circumference: the distance around the circle;
C = 2πr = πd. - Area: the two-dimensional space the circle encloses;
A = πr².
Real-world examples help connect the formulas to intuition: if a bicycle wheel has a radius of 0.35 m, its diameter is 0.70 m, the circumference is roughly the distance the bike travels in one full rotation (≈ 2.199 m using π ≈ 3.1416), and the area describes the surface of a perfectly round disk of the same size. In carpentry, machining, or 3D printing, these relationships convert between a measured diameter and the cut length (circumference) of a band, belt, or gasket. In science classes, switching π precision shows how rounding affects results and significant figures.
All calculations run entirely in your browser (client-side JavaScript), so inputs never leave your device. That means the calculator is fast, private, and works offline after it loads.
Circle Formulas
The four circle measures are linked by the radius. These sections show the direct formula, a plain-English method, and a quick example for common search cases.
Calculation note: Last updated June 23, 2026 by Starlight Tools. Formulas use standard Euclidean circle relationships: d = 2r, C = 2πr, and A = πr².
Rounded decimals use your decimal-place setting. Consistency checks allow the larger of display rounding, 1e-6 relative tolerance, or 1e-9 absolute tolerance.
How to find area of a circle
Square the radius, then multiply by π: A = πr².
- Divide the diameter by
2if the diameter is given. - Use
A = πr², orA = π(d/2)²directly. - Substitute the value, keep the exact π form if useful, then round.
Example: if r = 7, then A = π(7²) = 49π ≈ 153.94.
How to find circumference
Multiply the radius by 2π, or multiply the diameter by π: C = 2πr = πd.
- Start with the known radius
r. - Apply
C = 2πr. - Substitute the radius, keep the exact π form if needed, then round.
Example: if d = 10, then C = 10π ≈ 31.42.
How to find diameter
Double the radius, divide circumference by π, or use area: d = 2r = C/π = 2√(A/π).
Example: if A = 64, then d = 2√(64/π) ≈ 9.03.
How to find radius
Halve the diameter, divide circumference by 2π, or take the square root of area divided by π: r = d/2 = C/(2π) = √(A/π).
Example: if C = 18, then r = 18/(2π) = 9/π ≈ 2.86.
Circle Calculator: FAQs
Which inputs are valid to solve a circle?
Any one of radius, diameter, circumference, or area can solve the circle. If you enter more than one value, the calculator checks whether they agree within the rounding tolerance.
How do you find area from diameter?
Divide the diameter by 2 to get the radius, then use A = πr². Equivalently, A = π(d/2)².
How do you find radius from circumference?
Use r = C/(2π). Divide the circumference by twice pi to get the radius.
How do you find diameter from area?
Use d = 2√(A/π). First divide the area by pi, take the square root to find the radius, then double it.
Why is area in square units?
Area measures two-dimensional space, so a length unit is multiplied by itself. For example, centimeters become square centimeters, written cm².
What is the difference between circumference and diameter?
Diameter is the straight distance across the circle through its center. Circumference is the distance around the outside edge.
Should I use 3.14, 22/7, or Math.PI?
Use Math.PI for the most precise browser calculation. Use 3.14 or 22/7 only when your assignment or hand calculation expects that approximation.
Can I use different units for each value?
Yes. Radius, diameter, and circumference use length units, while area uses square units. The calculator converts the selected units before solving.
Does the calculator keep my data private?
Yes. Calculations run locally in your browser and no circle values are uploaded.
Common Circle Calculation Mistakes
Mixing radius and diameter
Diameter is twice the radius. If an answer is exactly twice or half what you expected, check whether the input was r or d.
Forgetting square units
Area is always in square units, such as cm² or ft², because it measures a two-dimensional surface.
Converting area like length
Length conversions and area conversions are different. For example, 100 cm = 1 m, but 10,000 cm² = 1 m².
Rounding too early
Keep the exact π form or extra decimal places until the final step, especially when a teacher or specification expects a rounded final answer.