Circle Calculator with Step-by-Step Working

Enter your radius, diameter, circumference, or area and instantly see all circle properties calculated with full working steps - perfect for checking your PSLE math homework!

Calculate Circle Properties

Enter any value you know about the circle, select your π value, and see all properties calculated with step-by-step working.

Circle Properties Calculator

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Value of π (as specified in question)

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Understanding Circle Properties

Circles are a fundamental topic in the PSLE Math syllabus. Before diving into formulas, let’s understand the key parts of a circle.

Parts of a Circle

Term	Definition	Symbol
Centre	The fixed point in the middle of the circle	O
Radius	Distance from the centre to any point on the circle	r
Diameter	A line through the centre, touching both sides (d = 2r)	d
Circumference	The distance around the circle (the perimeter)	C
Area	The space inside the circle	A

💡 Key Relationship

The diameter is always twice the radius: d = 2r. This means r = d ÷ 2. Always identify which one the question gives you!

The Magic Number: π (Pi)

Pi (π) is a special constant - the ratio of any circle’s circumference to its diameter. It’s approximately:

π ≈ 3.14 (most common in PSLE)
π ≈ 22/7 (useful when radius is a multiple of 7)
π = 3.14159265… (exact, goes on forever)

⚠️ PSLE Tip: Check Which π to Use!

Always read the question carefully. It will specify whether to use π = 3.14 or π = 22/7. Using the wrong value will give you the wrong answer!

Essential Circle Formulas

Here are the formulas you must memorize for PSLE:

Circumference (Distance Around)

$C = 2 \times \pi \times r$

Or equivalently:

$C = \pi \times d$

Memory trick: “Two pies are around” → 2πr

Area (Space Inside)

$A = \pi \times r^2$

Which means:

$A = \pi \times r \times r$

Memory trick: “Pie are squared” → πr²

💡 Squared vs. Not Squared

Circumference: radius is NOT squared (just 2πr)
Area: radius IS squared (πr²)

This is a common mistake! Area always has squared units (cm²).

Worked Examples

Example 1: Given Radius, Find All

Problem:

A circle has a radius of 7 cm. Using π = 22/7, find the circumference and area.

Step 1: Find the Circumference

$C = 2 \times \pi \times r$ $C = 2 \times \frac{22}{7} \times 7$ $C = 2 \times 22$ $C = 44 \text{ cm}$

Step 2: Find the Area

$A = \pi \times r^2$ $A = \frac{22}{7} \times 7 \times 7$ $A = \frac{22}{7} \times 49$ $A = 22 \times 7$ $A = 154 \text{ cm}^2$

Answer: Circumference = 44 cm, Area = 154 cm²

Example 2: Given Diameter, Find All

Problem:

A circular pond has a diameter of 10 m. Using π = 3.14, find the circumference and area.

Step 1: Find the Radius

$r = d \div 2 = 10 \div 2 = 5 \text{ m}$

Step 2: Find the Circumference

$C = \pi \times d$ $C = 3.14 \times 10$ $C = 31.4 \text{ m}$

Step 3: Find the Area

$A = \pi \times r^2$ $A = 3.14 \times 5 \times 5$ $A = 3.14 \times 25$ $A = 78.5 \text{ m}^2$

Answer: Circumference = 31.4 m, Area = 78.5 m²

Example 3: Finding Radius from Circumference

Problem:

A circular track has a circumference of 88 m. Using π = 22/7, find the radius.

Rearranging the formula:

From $C = 2 \times \pi \times r$ , we get:

$r = C \div (2 \times \pi)$ $r = 88 \div (2 \times \frac{22}{7})$ $r = 88 \div \frac{44}{7}$ $r = 88 \times \frac{7}{44}$ $r = 14 \text{ m}$

Answer: Radius = 14 m

Semicircles and Quarter Circles

PSLE often tests semicircles (half circles) and quarter circles. Here’s how to handle them:

Semicircle Formulas

Property	Formula
Area	$\frac{1}{2} \times \pi \times r^2$
Curved part (arc)	$\frac{1}{2} \times 2\pi r = \pi r$
Perimeter	$\pi r + 2r$ (arc + diameter)

❌ Common Mistake: Semicircle Perimeter

Many students forget that the perimeter of a semicircle includes the diameter (the straight edge), not just the curved part!

Wrong: Perimeter = πr (only the arc) Correct: Perimeter = πr + 2r (arc + diameter)

Quarter Circle Formulas

Property	Formula
Area	$\frac{1}{4} \times \pi \times r^2$
Curved part (arc)	$\frac{1}{4} \times 2\pi r = \frac{1}{2}\pi r$
Perimeter	$\frac{1}{2}\pi r + 2r$ (arc + two radii)

Common PSLE Mistakes to Avoid

⚠️ Mistake 1: Confusing Radius and Diameter

Always check whether the question gives you the radius or diameter. If given diameter, divide by 2 first to get radius!

⚠️ Mistake 2: Wrong Formula for Circumference vs Area

Circumference = 2πr (NOT squared)
Area = πr² (radius IS squared)

If your answer has cm², you calculated area. If it has cm, you calculated circumference.

⚠️ Mistake 3: Using Wrong π Value

PSLE questions specify which value of π to use. Using 3.14 when the question says 22/7 (or vice versa) will give you the wrong answer!

⚠️ Mistake 4: Forgetting Straight Edges

For semicircles and quarter circles, remember to include the straight edges (diameter or radii) when finding the perimeter!

Quick Reference Table

Given	To Find	Formula
Radius	Diameter	d = 2r
Diameter	Radius	r = d ÷ 2
Radius	Circumference	C = 2πr
Diameter	Circumference	C = πd
Radius	Area	A = πr²
Circumference	Radius	r = C ÷ (2π)
Area	Radius	r = √(A ÷ π)

Practice Tips for PSLE

Memorize the formulas: Know both versions of the circumference formula (2πr and πd)
Draw and label: Always sketch the circle and mark what’s given
Check your π: Circle the value of π in the question before starting
Units matter: Area uses square units (cm²), length uses linear units (cm)
Use the calculator above: Check your working by entering different values

More Circle Resources

Looking to practice more circle problems? Check out these guides:

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Circle Calculator: Area & Circumference with Step-by-Step Working

Circle Calculator with Step-by-Step Working

Calculate Circle Properties

Circle Properties Calculator

Understanding Circle Properties

Parts of a Circle

The Magic Number: π (Pi)

Essential Circle Formulas

Circumference (Distance Around)

Area (Space Inside)

Worked Examples

Semicircles and Quarter Circles

Semicircle Formulas

Quarter Circle Formulas

Common PSLE Mistakes to Avoid

Quick Reference Table

Practice Tips for PSLE

More Circle Resources

Master Circles with AI Practice

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