📏 Enter known values

📐 Accepted units: mm, cm, dm, m, dam, hm, km, in, ft, yd, mi

Formula Reference

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Worked example: Radius

Data
Diameter
\(b = {\color{#6c5ce7}{10\,\text{cm}}}\)
Radius
\(a = \,?\)
Formula
\[a = \frac{{b}}{2}\]
Steps
1Substitute the values
\[a = \frac{{\color{#6c5ce7}{10\,\text{cm}}}}{2}\]
Each letter is replaced by its value.
2Divide
\[a = \frac{{\color{#6c5ce7}{10\,\text{cm}}}}{2} = 5\,\text{cm}\]
\(\frac{10}{2} = 5\)
Radius: 5 cm
Check

If we use the result to calculate Diameter, we should get the value you entered:

\[b = 2\cdot{a}\]
\[b = 2\cdot5\,\text{cm} = 10\,\text{cm}\]
It gives 10 cm, the same as the value entered.

Worked example: Circumference

Data
Radius
\(a = {\color{#6c5ce7}{5\,\text{cm}}}\)
Circumference
\(c = \,?\)
Formula
\[c = 2\cdot\pi\cdot{a}\]
Steps
1Substitute the values
\[c = 2\cdot\pi\cdot{\color{#6c5ce7}{5\,\text{cm}}}\]
Each letter is replaced by its value.
2Multiply
\[c = 2\cdot\pi\cdot{\color{#6c5ce7}{5\,\text{cm}}} \approx 31.4159\,\text{cm}\]
\(2\cdot\pi \approx 6.2832\)\(6.2832\cdot5 \approx 31.4159\)
Circumference: 31.4159 cm

Worked example: Area

Data
Radius
\(a = {\color{#6c5ce7}{5\,\text{cm}}}\)
Area
\(d = \,?\)
Formula
\[d = \pi\cdot{{a}}^{2}\]
Steps
1Substitute the values
\[d = \pi\cdot{\left({\color{#6c5ce7}{5\,\text{cm}}}\right)}^{2}\]
Each letter is replaced by its value.
2Square
\[d = \pi\cdot25\,\text{cm}^{2}\]
\(5 \times 5 = 25\)\(\text{cm} \times \text{cm} = \text{cm}^{2}\)
3Multiply
\[d = \pi\cdot25\,\text{cm}^{2} \approx 78.5398\,\text{cm}^{2}\]
\(\pi\cdot25 \approx 78.5398\)
Area: 78.5398 cm²
If you know: Radius
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Diameter Circumference Area
If you know: Diameter
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Radius Circumference Area
If you know: Circumference
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Radius Diameter Area
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Radius Diameter Circumference

Circle formulas

A circle is defined by a single measurement: from the radius, the diameter, the circumference or the area you get the other three.

\[ d = 2r \]

\[ C = 2\pi r = \pi d \]

\[ A = \pi r^2 \]

And the other way round, to find the radius:

\[ r = \frac{d}{2} \]

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

\[ r = \sqrt{\frac{A}{\pi}} \]

How to use the calculator

  1. Enter the value you know: radius, diameter, circumference or area.
  2. Leave the other three fields empty.
  3. Press Calculate. You can type units (cm, m, cm²) and the results keep them.

Worked examples

1. From the diameter: d = 10 cm

The radius is half: \( r = 5 \) cm. Circumference \( C = 2\pi \times 5 \approx 31.42 \) cm and area \( A = \pi \times 5^2 \approx 78.54 \) cm².

2. Radius from the circumference: C = 50 cm

\[ r = \frac{50}{2\pi} \approx 7.96\ \text{cm} \]

So the diameter is \( \approx 15.92 \) cm and the area \( \approx 198.94 \) cm².

3. Diameter from the area: A = 100 m²

\[ r = \sqrt{\frac{100}{\pi}} \approx 5.64\ \text{m} \]

The diameter is \( \approx 11.28 \) m and the circumference \( \approx 35.45 \) m.

4. One 30 cm pizza or two 20 cm pizzas?

The 30 cm pizza has \( \pi \times 15^2 \approx 706.86 \) cm². Two 20 cm pizzas have \( 2 \times \pi \times 10^2 \approx 628.32 \) cm². The big one has more pizza.

Circumference and perimeter

The circumference is the line around the circle, and its length is the perimeter of the circle. That is why "circumference" and "perimeter of a circle" mean the same length: C = πd.

Table: diameter, circumference and area by radius

RadiusDiameterCircumferenceArea
1 cm2 cm6.28 cm3.14 cm²
2 cm4 cm12.57 cm12.57 cm²
3 cm6 cm18.85 cm28.27 cm²
4 cm8 cm25.13 cm50.27 cm²
5 cm10 cm31.42 cm78.54 cm²
6 cm12 cm37.7 cm113.1 cm²
7 cm14 cm43.98 cm153.94 cm²
8 cm16 cm50.27 cm201.06 cm²
9 cm18 cm56.55 cm254.47 cm²
10 cm20 cm62.83 cm314.16 cm²
15 cm30 cm94.25 cm706.86 cm²
20 cm40 cm125.66 cm1,256.64 cm²

When Do You Need the Circle Formulas?

🍕 Comparing Pizza and Cake Sizes

The size on the menu is the diameter, but what you eat is the area: a 30 cm pizza has 2.25 times the area of a 20 cm one.

Choose the best deal by area, not by diameter
🌱 Round Gardens and Pools

The area gives the soil, grass or pool cover you need, and the circumference gives the edging or fence.

Buy the right amount of material
🚲 Wheels and Tyres

Each turn of a wheel moves it one circumference forward: a 70 cm wheel covers about 2.2 m per turn.

Distances, speedometers and gear ratios
🔧 Pipes and Ducts

The cross-section area of a pipe tells how much fluid or air fits through it; doubling the diameter quadruples it.

Size pipes, hoses and vents
🪑 Tables, Rugs and Rooms

With the diameter of a round table or rug you know the floor area it covers and the trim around it.

Plan furniture and decoration
📚 Homework and Exams

Radius, diameter, circumference and area appear in almost every geometry course, often going from one to another.

Check your answers step by step

Common Mistakes

⚠️ Mixing Up Radius and Diameter
Common Error: Using the diameter as if it were the radius. With d = 10 cm, A = π × 10² = 314 cm² instead of 78.5 cm².
✅ Solution: Halve the diameter first: r = d ÷ 2
⚠️ Forgetting to Square the Radius
Common Error: Writing A = π × r instead of π × r². With r = 5 cm you get 15.7 instead of 78.5.
✅ Solution: The area always has the radius squared
⚠️ Confusing Circumference and Area
Common Error: Using 2πr to find the space inside, or πr² to find the length of the edge.
✅ Solution: Edge = circumference (cm); inside = area (cm²)
⚠️ Wrong Units for the Area
Common Error: Writing the area in cm instead of cm². The area of a circle measured in cm is in cm².
✅ Solution: Lengths in cm, areas in cm²
⚠️ Rounding π Too Early
Common Error: Using π = 3 gives errors of almost 5 %. With big circles the difference is noticeable.
✅ Solution: Use π ≈ 3.1416 or the π key, and round at the end
⚠️ Solving for the Radius Without the Root
Common Error: From A = 100 writing r = 100 ÷ π ≈ 31.8 and forgetting the square root (the radius is ≈ 5.64).
✅ Solution: r = √(A ÷ π): divide first, then take the root

Applications by Industry

Construction
  • Columns: Concrete for round columns from the diameter
  • Paving: Area of round patios and roundabouts
  • Formwork: Length of the edge of circular forms
Engineering
  • Pipes: Cross-section area and flow
  • Gears and pulleys: Circumference and speed ratios
  • Bearings: Diameters and tolerances
Food
  • Pizza and cakes: Area to compare sizes and prices
  • Baking pans: Adapting recipes to another pan size
  • Portions: Slices of the same area
Gardening & Landscaping
  • Flower beds: Soil and mulch for round beds
  • Irrigation: Area covered by a sprinkler of a given radius
  • Edging: Length of the border
Sports & Transport
  • Wheels: Distance per turn from the diameter
  • Courts: Circles and arcs on the field
  • Tracks: Length of curved lanes
Education
  • Geometry: The relations between radius, diameter, circumference and area
  • Pi: Measuring circles to estimate π
  • Exams: Problems that give one value and ask for another

External Resources

Other calculators

Area of a Circle
Area of a Circle
Area of a Trapezoid
Area of a Trapezoid
Area of a Triangle
Area of a Triangle
Area of a Rectangle
Area of a Rectangle
Area of a Square
Area of a Square
Area of a Rhomboid
Area of a Rhomboid
Area of a Rhombus
Area of a Rhombus
Area of a Quadrangular Prism
Area of a Quadrangular Prism

Geometry Calculators

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