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Circle Calculator: Radius, Diameter, Circumference & Area

Solve for radius, diameter, circumference, and area from any one value.

Circle Inputs

Decimal places4
Result
Radius (r)5 m
Diameter (d)10 m
Circumference (C)31.4159 m
Area (A)78.5398 m²

How it was calculated

  • From radius r = 5 m:
  • Diameter: d = 2r = 2 × 5 = 10 m
  • Circumference: C = 2πr = 2π × 5 ≈ 31.4159 m
  • Area: A = πr² = π × (5)² ≈ 78.5398 m²

Formulas used

d = 2r, diameter is twice the radius

C = 2πr, circumference

A = πr², area

From circumference: r = C/(2π), A = C²/(4π)

From area: r = √(A/π), C = 2√(πA)

When and How to Use Circle Results

Which input to use when, formulas and definitions are in the article below. Trusted by students and educators for geometry and construction. All calculations run locally.

Workflow Tips

When You Know the Radius

Use when you measured from center to edge (e.g. round table, circular plot).

When You Know the Diameter

Use when "across" is easier than radius (pipes, wheels, round objects).

When You Know the Circumference

Use when you have the distance around (e.g. tape around a cylinder).

When You Know the Area

Use when you have square units (e.g. floor area of a round room).

Circle Calculator: Radius, Diameter, Circumference & Area

Free circle calculator: find radius, diameter, circumference, or area from one value. Area of a circle formula, how to find circumference, diameter of a circle. Circle geometry solver, units: mm, cm, m, in, ft. Trusted by students and educators. No sign-up, all calculations run locally.

How to Use This Calculator

Select which circle measurement you already know—radius, diameter, circumference, or area—from the dropdown at the top. Enter the numeric value in the input field and choose a unit (mm, cm, m, in, or ft). The calculator instantly solves for all four properties: radius, diameter, circumference, and area. Linear results appear in your chosen unit; area appears in that unit squared (for example, m² or ft²). Adjust the precision slider between 2 and 10 decimal places to control how many digits display in the results. The “How it was calculated” section below the results shows the exact formulas used, so you can verify the math or reference it for homework. No button press is needed—results update live as you type.

What This Calculator Does & Who It's For

Calculator Purpose & Ideal Users

This circle calculator solves for r, d, C, and A from any one known value.
  • What You'll Get:
    Radius, diameter, circumference, area: All four from one input. Unit support: mm, cm, m, in, ft (linear and area in that unit squared). Precision: 2–10 decimal places. Step-by-step: “How it was calculated” shows the formulas used. Diagram: Parts of a circle (radius, diameter, circumference) for reference.
  • Ideal Users:
    Students & geometry: “Find the area of a circle from circumference,” “diameter of a circle from radius,” homework and exams. Teachers & curriculum: Quick checks and circle formula practice. DIY & construction: Round areas, edging, or circular layouts in your chosen unit. Anyone needing one circle measure from another: No need to memorize formulas, enter one value, get the rest.
  • Scope & Limits:
    Solves only r, d, C, and A from one another. Does not compute chord length, sector area, or arc length (those require angles); the article below explains radius, diameter, chord, tangent, and sector for context. Uses high-precision π (Math.PI) for accuracy. All calculations run in your browser; no data is sent to servers.

What Is a Circle Calculator? Circle Geometry Solver

A circle calculator (or circle geometry solver) finds radius (r), diameter (d), circumference (C), and area (A) from any single known value, enter one, get the other three. Use it to calculate area of a circle from circumference, find diameter of a circle from radius, or apply A = πr². See above for what you'll get and who it's for. Free online, no sign-up.

The Constant π (Pi)

Pi (π) is the ratio of a circle's circumference to its diameter:
π=C/d\pi = C/d
≈ 3.14159. It is the same for every circle, so
C=2πrC = 2\pi r
and
A=πr2A = \pi r^2
The calculator uses high-precision π so results are accurate to the decimal places you choose (2–10)
  • Circumference:
    C=2πrC = 2\pi r
  • Area:
    A=πr2A = \pi r^2
  • From C:
    r=C2πr = \frac{C}{2\pi}
  • From A:
    r=A/πr = \sqrt{A/\pi}

Parts of a Circle: Radius, Diameter, Chord, Tangent, Sector

What This Calculator Solves

This tool solves only for r, d, C, and A from one another. The terms below (radius, diameter, chord, tangent, sector) are for context; the calculator does not compute chord length or sector area.

Radius (r)

Distance from the center of the circle to any point on the edge. The calculator uses radius as the base for all formulas (d = 2r, C = 2πr, A = πr²).
  • Definition:
    Half the diameter; the "length from center to edge"

Diameter (d)

Distance across the circle through the center. d = 2r. Often easier to measure on physical objects than radius.
  • Definition:
    Twice the radius; the longest chord

Chord

A line segment whose endpoints lie on the circle. The diameter is a chord that passes through the center.
  • Note:
    This calculator does not solve for chord length; it solves for r, d, C, and A from one known value.

Tangent

A line that touches the circle at exactly one point, perpendicular to the radius at that point.
  • Note:
    Used in geometry and trigonometry; not required for the radius–diameter–circumference–area solver.

Sector

A "pie slice" of the circle bounded by two radii and an arc. Area of sector = (θ/360°) × πr², where θ is the angle in degrees.
  • Note:
    For full-circle area use A = πr²; for a sector use an area calculator that supports angles.

How to Calculate the Area of a Circle: Area of a Circle Formula

The area of a circle formula is
A=πr2A = \pi r^2
How to calculate the area of a circle: if you know the radius, use A = πr². If you know the diameter, use
A=π(d/2)2A = \pi(d/2)^2
If you know the circumference, use
A=C24πA = \frac{C^2}{4\pi}
How to find circumference from area: use
C=2πAC = 2\sqrt{\pi A}
This circle calculator does all of that from one value, enter radius, diameter, circumference, or area and get the other three; choose unit (m, ft, etc.) so area shows in that unit squared (m², ft²).
  • From radius:
    A=πr2A = \pi r^2
  • From diameter:
    A=π(d/2)2A = \pi(d/2)^2
  • From circumference:
    A=C24πA = \frac{C^2}{4\pi}

Circle Calculator FAQ

How do you find the circumference of a circle?

Circumference is the distance around the circle. Use
C=2πrC = 2\pi r
or
C=πdC = \pi d
For example, if the radius is 5 m, circumference ≈ 31.42 m. The calculator finds circumference from radius, diameter, or area automatically

What is the relationship between radius and diameter?

The diameter is exactly twice the radius:
d=2rd = 2r
So if you know the radius, double it for the diameter; if you know the diameter, halve it for the radius. The calculator uses this relationship to solve for all circle properties from any one known value

How many degrees are in a circle?

A full circle is 360 degrees (360°). In radians, another common unit for angles, a full circle is 2π radians (about 6.28). The circle calculator works with linear measures (radius, diameter, circumference) and area; for sector or arc calculations you would use the angle in degrees or radians.

How do I calculate the area of a circle from circumference?

From circumference C, first find the radius:
r=C2πr = \frac{C}{2\pi}
Then area
A=πr2A = \pi r^2
Or use
A=C24πA = \frac{C^2}{4\pi}
In this calculator, select "Circumference" as your known variable, enter C, and the tool will show area (and radius, diameter) with your chosen precision and units

What is pi (π) and why is it used for circles?

Pi (π) is the ratio of a circle's circumference to its diameter: π = C/d ≈ 3.14159. It is the same for every circle. That’s why circumference = πd = 2πr and area = πr². The calculator uses high-precision π (Math.PI) so results are accurate to many decimal places.

Can I use different units (mm, cm, m, in, ft)?

Yes. Choose your unit from the dropdown; the calculator converts everything internally. Linear results (radius, diameter, circumference) are shown in that unit; area is shown in that unit squared (e.g. m², ft², in²).

Mathematical Reference Note

Calculation Logic: This tool uses standard mathematical algorithms. While we strive for accuracy, errors in logic or user input can result in incorrect data.

Verification: Results should be cross-checked if used for important academic, professional, or personal calculations.

Standard Terms: This tool is provided free of charge and as-is. CalcRegistry provides no warranty regarding the accuracy or fitness of these results for your specific needs.

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