Circle Calculator for Radius, Diameter, Circumference and Area
Enter one known circle measurement and solve the other three. Get exact π, inverse-π and square-root forms, clear decimal values, correct length and area units, and every formula step in one place.
Last Updated: July 26, 2026
Calculate a Circle from One Known Value
Choose what you know. Radius, diameter and circumference use a linear input unit. Area uses the square of the selected input unit.
Your four circle measurements and calculation steps will appear here.
Calculation steps
- Choose the known measurement, enter its value and select Calculate Circle.
Circle measurements in common units
| Result unit | Radius | Diameter | Circumference | Area |
|---|---|---|---|---|
| Calculate with a physical unit to see conversions. | ||||
| Area unit | Converted area |
|---|---|
| Calculate with a physical unit to see area-only conversions. | |
Recent calculations
- Your last six results will appear here.
What Is a Circle Calculator?
A circle calculator converts one known measurement into the complete set of basic circle measurements. You can start with radius, diameter, circumference or area. The tool then finds the other three values, keeps an exact symbolic answer where one exists, and shows a rounded decimal for practical use.
This page focuses on one search intent: solving a circle from one known value. It does not add sector angles, arc lengths, annuli, chords, spheres or cylinders. Those problems need different inputs and formulas. Keeping the scope narrow makes the result easier to check and avoids mixing two-dimensional circle measurements with three-dimensional geometry.
The calculation runs in your browser. Your input and recent result history are not sent to a calculation server. Standard website analytics may record a page visit, but the calculator itself does not submit the entered measurement.
How to Use This Circle Calculator
- Select the measurement you already know: radius, diameter, circumference or area.
- Choose the base input unit. If you select area, the entered value uses the square of that unit.
- Enter a nonnegative number. You may use a decimal, fraction, proper mixed number or scientific notation.
- Select the output length unit and the number of decimal places.
- Select Calculate Circle. Read the exact result first, then use the decimal value if your work requires rounding.
For example, if you choose centimetres and enter a radius of 7, the calculator reads the input as 7 cm. It returns diameter and circumference in centimetres and area in square centimetres. If you switch the known measurement to area, a value of 7 uses cm² instead.
Circle Formulas Used by the Calculator
The formulas depend on the known value. Here, r is radius, d is diameter, C is circumference and A is area.
| Known value | Radius | Diameter | Circumference | Area |
|---|---|---|---|---|
| Radius r | r | 2r | 2πr | πr² |
| Diameter d | d/2 | d | πd | πd²/4 |
| Circumference C | C/(2π) | C/π | C | C²/(4π) |
| Area A | √(A/π) | 2√(A/π) | 2√(πA) | A |
Radius and diameter relationship
The diameter crosses the entire circle through its centre. It is exactly twice the radius. Use d = 2r when radius is known, or r = d/2 when diameter is known. This relationship does not involve π, so rational inputs remain exact rational outputs.
Circumference formula
Circumference is the distance around the circle. Use C = 2πr or C = πd. Because π is irrational, the exact result normally contains π. A decimal such as 43.982297 cm is a rounded approximation, not a replacement for the exact value 14π cm.
Circle area formula
Area measures the two-dimensional region inside the boundary. Use A = πr². Squaring the radius also squares its unit. A radius in metres produces area in square metres, while a radius in feet produces area in square feet.
Worked Circle Examples
Example 1: radius of 7 cm
Start with r = 7 cm. The diameter is 2 × 7 = 14 cm. Circumference is 2π × 7 = 14π cm, approximately 43.982297 cm. Area is π × 7² = 49π cm², approximately 153.93804 cm².
Example 2: circumference of 10 units
Start with C = 10. Radius is 10/(2π) = 5/π, approximately 1.591549. Diameter is 10/π, approximately 3.183099. Area is 10²/(4π) = 25/π, approximately 7.957747 square units.
Example 3: area of 1 square unit
Start with A = 1. Radius is √(1/π), approximately 0.56419 units. Diameter is twice that value, approximately 1.128379 units. Circumference is 2√π, approximately 3.544908 units. The square-root and π forms preserve the exact relationships.
Exact Answers, π and Decimal Rounding
The calculator separates exact symbolic results from decimal displays. If the input is radius 3/2, it keeps the exact circumference as 3π and the exact area as 9π/4. The decimal values are then calculated from a 120-place π constant and rounded only for display.
Starting from circumference introduces division by π. Starting from area introduces both π and a square root. These are still exact symbolic answers. For example, a circumference of 10 gives radius 5/π, while an area of 9 gives radius √(9/π). The calculator does not falsely label these irrational values as exact decimals.
The precision selector controls the maximum number of displayed decimal places. It does not change the entered fraction, the exact formula or the unit conversion. Very large and very small values switch to scientific notation so a positive result does not appear as zero and does not overflow into Infinity.
Circle Unit Conversion
Length and area do not convert in the same way. A linear conversion factor applies once to radius, diameter and circumference. It applies twice to area. Since 1 m equals 100 cm, 1 m² equals 100 × 100, or 10,000 cm².
The calculator uses exact international conversion definitions for inches, feet, yards and miles. For example, 1 inch is exactly 0.0254 metres, and 1 foot is exactly 0.3048 metres. It derives every converted circle from the unrounded input, not from a shortened decimal result.
Generic units are useful for textbook problems without a named physical unit. When you select generic units, the calculator labels outputs as units and square units. It hides physical conversions because there is no defined relationship between a generic unit and metres, inches or feet.
Common Circle Calculation Mistakes
- Using diameter as radius: divide diameter by 2 before applying a radius-based formula.
- Forgetting square units: circumference uses cm or m, while area uses cm² or m².
- Rounding π too early: keep π or full precision until the final decimal step.
- Mixing input units: confirm whether a source measurement is millimetres, centimetres, inches or another unit.
- Entering a formula instead of a value: choose the correct mode, then enter only its numeric measurement.
- Assuming a negative radius is meaningful: geometric circle measurements must be nonnegative.
When This Calculator Is Useful
You can use the tool for school geometry, circular labels, pipes, wheels, garden layouts, table tops, craft projects and preliminary material estimates. Measure the most reliable dimension available, select its matching mode, and let the calculator derive the remaining values.
Real objects introduce measurement tolerance, thickness and manufacturing variation. A calculated circle is mathematically exact for the entered number, but the physical result is only as accurate as the measurement. Keep enough significant digits for the task and verify safety-critical engineering or construction work with the required professional standard.
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Frequently Asked Questions
What does a circle calculator calculate?
This calculator uses one known radius, diameter, circumference or area to find all four circle measurements. It shows exact symbolic forms, decimal values, formulas and unit conversions.
How do I find diameter from radius?
Multiply the radius by 2. The formula is d = 2r, so a circle with radius 7 cm has diameter 14 cm.
How do I find radius from diameter?
Divide the diameter by 2. The formula is r = d/2, so a diameter of 10 inches gives a radius of 5 inches.
What is the circumference formula?
Use C = 2πr when the radius is known, or C = πd when the diameter is known. Circumference is a length and uses a linear unit.
What is the circle area formula?
Use A = πr². When diameter is known, the equivalent formula is A = πd²/4. Area uses a square unit such as cm², m² or ft².
How do I find radius from circumference?
Divide circumference by 2π: r = C/(2π). A circumference of 10 units gives the exact radius 5/π units.
How do I find radius from circle area?
Divide the area by π, then take the principal square root: r = √(A/π). Only the nonnegative radius is used for a geometric circle.
Why does an exact circle answer contain pi?
π is irrational, so most circle circumferences and areas cannot be written as terminating decimals. Keeping π in the answer preserves the exact mathematical value.
What is the difference between circumference and area?
Circumference measures distance around the boundary and uses linear units. Area measures the region inside the circle and uses square units.
Can I enter fractions and scientific notation?
Yes. The value field accepts integers, decimals, fractions, proper mixed numbers and scientific notation. It does not evaluate typed π symbols, variables or formulas.
How are circle units converted?
Radius, diameter and circumference use the linear conversion factor once. Area uses the square of that factor, so converting 1 m² to cm² gives 10,000 cm².
What happens when the value is zero or negative?
Zero is accepted as a degenerate circle and returns exact zero for all four measurements. Negative radius, diameter, circumference and area values are rejected.
Mathematical note: Results follow standard Euclidean circle formulas and the selected units. Decimal values are rounded displays. Verify important academic, construction, engineering or commercial work independently.