Circle Calculator: Radius, Area & More

Example: radius 5 m (default)

By default (radius 5 m, 4 decimal places), you get diameter 10 m, circumference ≈ 31.4159 m, and area ≈ 78.5398 m². Change the “known” dropdown if you measured diameter, distance around, or square footage instead.

Which input to pick

Radius

Center to edge: round tables, sprinkler reach, hole radius.

Diameter

Straight across through the center: wheels, pipes, lids when “across” is easier to measure.

Circumference

Tape around the outside: hose length for a ring, border trim, tree trunk.

Area

Already in square units: round patio slab, circular lawn patch from a plan.

Circle calculator: r, d, circumference, and area from one value

One measurement in, four out, with units and a diagram. Chord and sector formulas are reference only; this tool does not take an angle.

What This Calculator Does

Enter one of radius, diameter, circumference, or area (with a unit). The page returns the other three, shows a labeled circle sketch, and prints step-by-step algebra in the results panel. Handy for homework checks, quick job-site math, or flipping between “across” and “around” measurements.

Good for:

“I know the diameter is 10 ft; what’s the area?” or verifying A = πr² by hand.
Not for:

Chord length, tangent lines, arc length, or sector area (those need angles). Ellipses and ovals are different shapes.

How the Math Works

Everything reduces to radius in meters internally, then converts back to your unit.

From radius r:

$d = 2r,\quad C = 2\pi r,\quad A = \pi r^2$
From diameter d:

$r = \frac{d}{2}$
From circumference C:

$r = \frac{C}{2\pi},\quad A = \frac{C^2}{4\pi}$
From area A:

$r = \sqrt{\frac{A}{\pi}},\quad C = 2\sqrt{\pi A}$
Worked example (defaults):

Known r = 5 m → d = 10 m, C ≈ 31.4159 m, A ≈ 78.5398 m².

How to Use This Calculator

Results update live; no calculate button. If the input is zero or negative, the tool waits for a valid number. Switch units anytime; only the label changes, not the geometry.

Precision slider:

Controls displayed decimals (2–10); underlying math still uses full floating-point π.
Diagram:

Scales the drawing for visibility; numeric results are the source of truth, not the SVG size.

Parts of a Circle (Reference)

Radius is center to rim; diameter crosses through the center. A chord connects two rim points (diameter is the longest chord). A tangent touches at one point, perpendicular to the radius there. A sector is a pie slice: area = (θ/360°) × πr² when θ is in degrees. This solver only links r, d, C, and A for a full circle.

Circle Calculator FAQ

How do you find the circumference of a circle?

Distance around the circle is

C = 2\pi r

or

C = \pi d

. With the default radius 5 m, circumference is about 31.42 m. Pick circumference as the known value if you measured around a pipe or rim instead of across it.

What is the relationship between radius and diameter?

Diameter is twice the radius:

d = 2r

. Halve the diameter when you only measured across; double the radius when you measured from the center to the edge.

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

From C, radius is

r = \frac{C}{2\pi}

then

A = \pi r^2

, or use

A = \frac{C^2}{4\pi}

directly. Choose Circumference in the dropdown, enter C, and the tool fills radius, diameter, and area in your unit.

How many degrees are in a circle?

A full turn is 360°, or 2π radians (~6.28 rad). This calculator handles linear measures and area only; arc length and sector area need a central angle and a different tool.

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

π is the ratio of circumference to diameter, the same for every circle:

\pi = \frac{C}{d}

≈ 3.14159. That is why

C = 2\pi r

and

A = \pi r^2

. The page uses Math.PI and your chosen decimal places (2–10).

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

Yes. Linear outputs use the unit you pick; area shows that unit squared (m², ft², in², etc.). Conversions run internally through meters so mixed typing is not needed.

Sources & citations

References used for the calculation method and definitions. Links open in a new tab when available.

[1]

NIST – The International System of Units (SI)

SI base and derived units (meter, etc.) used for internal length and area conversions in the calculator.

[2]

MathWorld – Circle

Standard definitions of radius, diameter, circumference, and area relations for a circle.

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.

Circle Calculator: Radius, Diameter, Circumference & Area

Circle Inputs

How it was calculated

Formulas used