Area of a Sector Formula Explained, With Examples
Every area of a sector result comes from one formula. Once you understand what goes into it, you can sanity-check any figure you are given, whether by an employer, a bank, a teacher or another website.
The formula
(θ/360) × πr²
What each input means
- Radius: the value you enter in the calculator.
- Angle (degrees): the value you enter in the calculator.
Example
For example, with these inputs:
- Radius: 5
- Angle (degrees): 60
the calculator returns:
- Area: 13.09
How the result changes
The table keeps the other inputs at their example values and changes radius.
| Radius | Area |
|---|---|
| 5 | 13.09 |
| 2.5 | 3.2725 |
| 3.75 | 7.3631 |
| 6.25 | 20.4531 |
| 7.5 | 29.4524 |
Why it matters
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
In everyday life the same maths shows up in discounts, recipe scaling, renovation measurements and comparing prices per unit. Being comfortable with it saves money and avoids costly measuring mistakes.
Each formula has assumptions built in. Area formulas assume flat shapes, volume formulas assume regular solids and statistical measures assume the data you enter is the data you want to describe. Knowing the assumptions helps you pick the right tool.
These calculations appear throughout the Singapore syllabus, from primary school percentages and fractions to secondary school algebra and geometry. Understanding the formula makes problem sums easier because you can recognise which quantity is missing.
Related calculations
- What Percent Is X of Y: Finds what percentage one number is of another.
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- Percentage Decrease Calculator: Subtracts a percentage from a number.
Use the Area of a Sector Calculator to plug in your own numbers.
Run your own numbers: Area of a Sector Calculator