How to Calculate Area of a Sector: A Step-by-Step Guide
Calculates the area of a sector from the measurements you enter. Use any unit, as long as all inputs use the same one.
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.
What you need
- Radius
- Angle (degrees)
Step by step
- Enter the radius.
- Enter the angle (degrees).
- The results update as you type, or press Calculate.
- Read the area first, then the supporting figures below it.
The formula
(θ/360) × πr²
Worked example
For example, with these inputs:
- Radius: 5
- Angle (degrees): 60
the calculator returns:
- Area: 13.09
A second example
Now change the inputs to:
- Radius: 6.25
- Angle (degrees): 60
the calculator returns:
- Area: 20.4531
Practical tips
- Write down the formula before plugging numbers in; it prevents mixing up variables.
- Estimate the answer roughly first so you can spot a result that is clearly wrong.
- When numbers are very large or small, scientific notation makes them easier to compare.
- Use brackets to make the order of operations explicit.
Background
A quick mental estimate before calculating is a powerful check. If a room's floor area comes out at 4,000 square metres or a percentage comes out above 100% when it should not, you know to look again.
Calculators are best used to check working rather than replace it, especially for exams where method marks count. Work the problem by hand first, then confirm with the calculator.
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
Related calculations
- What Percent Is X of Y: Finds what percentage one number is of another.
- Percentage Change Calculator: Calculates the percentage increase or decrease.
- Percentage Increase Calculator: Adds a percentage to a number.
- Percentage Decrease Calculator: Subtracts a percentage from a number.
Want to skip the arithmetic? The free Area of a Sector Calculator does all of this instantly and updates as you type.
Run your own numbers: Area of a Sector Calculator