How do I find the area of a circle from its diameter?

Use A = pi x d squared / 4. Square the diameter, multiply by pi, then divide by 4. For example, a diameter of 10 gives A = pi x 100 / 4, which is about 78.54 square units.

How do I find the radius if I only know the circumference?

Divide the circumference by 2 pi: r = C / 2 pi. A circumference of 31.42 gives r = 31.42 / 6.28318, which is about 5. You can then get the diameter with d = 2r.

What is the difference between circumference and perimeter of a circle?

There is none. They are the same distance around the shape. Circumference is simply the specific name used for a circle's perimeter, because its boundary is a single curved line.

Can I calculate a circle's area from its circumference?

Yes. First find the radius with r = C / 2 pi, then apply A = pi r squared. Alternatively use the direct formula A = C squared / 4 pi to go straight from circumference to area.

What units does the circle calculator use?

Any consistent unit you like. Enter your value in cm, m, inches, or feet and the radius, diameter, and circumference come back in that same unit, while the area is given in squared units.

No. 3.14 is just a rounded value. Pi is an irrational number that begins 3.14159265 and never ends or repeats, so 3.14 is an approximation, not the exact value.

Circle Calculator

Formula

Enter your values

Enter your values and press Calculate — your answer, visual and step-by-step solution appear here.

This circle calculator finds a circle's area, circumference, radius, and diameter from any single value you know. Enter just one measurement and the tool instantly returns the other three, alongside a labeled diagram and the exact formula it used. It is free, works without a login, and shows every step so you can learn the math, not just copy the answer. Looking for other tools? Browse all MathInSite calculators.

How to Use This Circle Calculator

You only need one known measurement to solve the entire circle. Follow these steps:

Pick the value you know. Choose whether you are entering the radius, diameter, circumference, or area. The calculator works from any one of the four.
Enter your number. Type the measurement into the matching field. Use the same length unit throughout (cm, m, inches, feet) so the results stay consistent.
Press Calculate. The tool computes the remaining three properties at once using the standard circle formulas.
Read every result. Review the radius, diameter, circumference, and area together, plus the worked steps and the formula applied. Remember area is reported in square units while radius, diameter, and circumference share your input's linear unit.

Tip: Want to learn first? Use the Hint button to try the problem yourself, then reveal the full step-by-step solution.

Circle Formulas (Radius, Diameter, Circumference, Area)

Every circle is governed by a small set of formulas built on the radius (r), diameter (d), and the constant π (pi). Once you know any one property, you can derive the rest. The table below lists the core circle formulas in both standard and "in terms of π" form.

Property	Formula	In terms of π
Diameter (d)	d = 2r	d = 2r
Radius (r)	r = d / 2	r = C / 2π
Circumference (C)	C = 2πr	C = πd
Area (A)	A = πr²	A = πd² / 4 = C² / 4π

In plain terms: the diameter is always twice the radius, so the radius is half the diameter. The circumference (the distance around the circle) equals 2πr, which is the same as π times the diameter. The area of a circle equals π times the radius squared — and because the diameter and circumference are tied to the radius, you can also write area as πd²/4 or C²/4π.

A = πr² C = 2πr = πd d = 2r

Parts of a Circle

Knowing the parts of a circle makes the formulas click. The diagram beside this calculator labels the key lines; here is what each term means.

Term	Definition
Center	The fixed point in the middle, equidistant from every point on the circle.
Radius	A straight line from the center to any point on the circle; equals half the diameter.
Diameter	A straight line through the center connecting two points on the circle; the longest chord and twice the radius.
Circumference	The total distance around the circle — its perimeter.
Chord	Any straight line joining two points on the circle (a diameter is a chord that passes through the center).
Arc	A curved portion of the circumference between two points.
Sector	A "pie slice" region bounded by two radii and the arc between them.
Segment	The region between a chord and the arc it cuts off.
Tangent	A line that touches the circle at exactly one point.
Secant	A line that crosses the circle at two points.

Need the area or perimeter of squares, triangles, or rectangles instead? Use our area and perimeter of other shapes calculator. For sectors, arcs, and 3D shapes built from a circle, see the linked tools further down.

What Is Pi (π)?

Pi (π) is the ratio of any circle's circumference to its diameter — divide the distance around a circle by the distance across it and you always get π, no matter how big or small the circle is. Its value is approximately 3.14159…, and it never ends or repeats because π is an irrational (and transcendental) number.

This constant is what links a circle's straight-line measurements (radius and diameter) to its curved ones (circumference and area), which is why π appears in every circle formula. Pi also sits at the heart of trigonometry — explore that connection with our trig functions and the unit circle calculator.

Value of pi: π ≈ 3.14159265… For everyday work 3.14 or 3.1416 is close enough, but this calculator uses the full precision built into your device.

How to Find Each Property

Here is how to compute each of the four circle properties by hand, with a worked example for every case. Throughout, we use a circle with radius r = 5 cm.

How to Find the Circumference of a Circle (find C)

Use C = 2πr, or C = πd if you know the diameter. The circumference is the distance once around the circle.

Identify the radius. r = 5 cm (or use d ÷ 2 if you only have the diameter).
Multiply by 2π. C = 2 × π × 5 = 10π.
Evaluate. C = 10 × 3.14159 ≈ 31.42 cm.

How to Find the Area of a Circle (find A)

Use A = πr². The area of a circle is the space enclosed inside the circumference, measured in square units.

Identify the radius. r = 5 cm.
Square it. r² = 5² = 25.
Multiply by π. A = π × 25 ≈ 78.54 cm².

How to Find the Radius of a Circle (find r)

You can find the radius of a circle from any other property: r = d ÷ 2, r = C ÷ 2π, or r = √(A ÷ π).

Start from the known value. Suppose the area A = 78.54 cm².
Divide by π. A ÷ π = 78.54 ÷ 3.14159 ≈ 25.
Take the square root. r = √25 = 5 cm.

How to Find the Diameter of a Circle (find d)

Find the diameter of a circle with d = 2r, d = C ÷ π, or d = 2√(A ÷ π).

Start from the known value. Suppose the circumference C = 31.42 cm.
Divide by π. d = C ÷ π = 31.42 ÷ 3.14159 ≈ 10 cm.
Check with the radius. d = 2r = 2 × 5 = 10 cm. ✓

Worked Example — Solve a Circle Step by Step

Suppose you measure only the circumference of a circle as C = 31.42 cm and want the radius, diameter, and area. Try it yourself first, then check each step below.

Find the radius. Rearrange C = 2πr to r = C ÷ 2π = 31.42 ÷ (2 × 3.14159) = 31.42 ÷ 6.28318 ≈ 5 cm.
Find the diameter. d = 2r = 2 × 5 = 10 cm (equivalently, d = C ÷ π = 31.42 ÷ 3.14159 ≈ 10 cm).
Find the area. A = πr² = 3.14159 × 5² = 3.14159 × 25 ≈ 78.54 cm².
State the answer. A circle with circumference 31.42 cm has radius 5 cm, diameter 10 cm, and area 78.54 cm².

Why this works: Because every property depends only on the radius, finding r first unlocks all the others through d = 2r and A = πr².

Real-World Uses of a Circle Calculator

Circle math shows up far beyond the classroom. Common uses include:

Geometry homework — check area, circumference, radius, and diameter answers instantly.
Engineering and CNC — size round parts, bolt circles, and machined holes from a single dimension.
Landscaping and fencing — work out the area of circular gardens, patios, or ponds; pair it with the area and perimeter of other shapes tool for mixed layouts.
Cooking and furniture — compare pizza sizes or fit a round tabletop or rug to a room.
Graphic and product design — set precise dimensions for circular logos, buttons, and labels.

Common Mistakes

Mistake — Confusing radius and diameterThe radius is half the diameter. Plugging the diameter into A = πr² instead of the radius quadruples your area. Always confirm which measurement you have: r = d ÷ 2.

Mistake — Forgetting to square the radius for areaArea is A = πr², not πr. Square the radius before multiplying by π. With r = 5, that is π × 25 = 78.54, not π × 5 = 15.71.

Mistake — Using the wrong units on areaArea is always in square units (cm², m², in²), while radius, diameter, and circumference use plain linear units. Label area results with the squared unit.

Mistake — Rounding π too earlyUsing π ≈ 3.14 (or worse, 22/7) and rounding mid-calculation compounds error. Keep full precision until the final step, then round once.

Mistake — Squaring the diameter without dividing by 4When finding area from the diameter, use A = πd² ÷ 4, not πd². Skipping the ÷ 4 overstates the area by a factor of four.

Frequently Asked Questions

How do I find the area of a circle from its diameter?

Use A = πd² ÷ 4. Square the diameter, multiply by π, then divide by 4. For example, a diameter of 10 gives A = π × 100 ÷ 4 ≈ 78.54 square units.
How do I find the radius if I only know the circumference?

Divide the circumference by 2π: r = C ÷ 2π. A circumference of 31.42 gives r = 31.42 ÷ 6.28318 ≈ 5. You can then get the diameter with d = 2r.
What is the difference between circumference and perimeter of a circle?

There is none — they are the same distance around the shape. Circumference is simply the specific name used for a circle's perimeter, because its boundary is a single curved line.
Can I calculate a circle's area from its circumference?

Yes. First find the radius with r = C ÷ 2π, then apply A = πr². Alternatively use the direct formula A = C² ÷ 4π to go straight from circumference to area.
What units does the circle calculator use?

Any consistent unit you like. Enter your value in cm, m, inches, or feet and the radius, diameter, and circumference come back in that same unit, while the area is given in squared units.
Is pi exactly 3.14?

No. 3.14 is just a rounded value. Pi is an irrational number that begins 3.14159265… and never ends or repeats, so 3.14 is an approximation, not the exact value.