What is the Area Of Sector Calculator?
Cut a slice from a round pizza and you are holding a sector: two radii and the arc between them, the fundamental wedge of circular geometry. Its area is a fixed fraction of the whole circle's area, and that fraction is the central angle over 360° — so A = (θ/360°) × πr². A 60° slice of a radius-5 circle is one-sixth of the pie: (60/360) × π × 25 ≈ 13.09. Enter the Radius and the Central Angle (degrees) and read the Area result. The most common slip is entering the angle in radians while the calculator expects degrees, or vice versa — a 60° angle entered as 60 radians would produce nonsense. Sectors show up in pie charts, windshield wiper coverage, sprinkler spray patterns, and anywhere a rotating arm sweeps an area. As a bonus check, the sector's arc length is (θ/360°) × 2πr, so the same two inputs describe the slice's curved edge too.
With the pre-filled defaults — Radius 5, Central Angle (degrees) 60 — the Area Of Sector Calculator returns Area 13.0900. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Area Of Sector Calculator
- 1Type the circle's radius in the Radius field — try 5.
- 2Type the wedge angle in the Central Angle (degrees) field — try 60.
- 3Read the Area result: about 13.09.
- 4Confirm your angle is in degrees, not radians.
- 5Test 360° to verify you get the full circle's area, about 78.54.
Formula
This is the core equation the Area Of Sector Calculator uses to calculate results. Enter values in the calculator above to see it in action.
See the full step-by-step formula guide with worked examples →
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| Example calculation | Radius = 5, Central Angle (degrees) = 60 | Area = 13.0900 |
Value Reference Table
See how the Area changes as Radius moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Radius | Area |
|---|---|
| 1 | 0.5236 |
| 3 | 4.7124 |
| 4 | 8.3776 |
| 5 | 13.0900 |
| 6 | 18.8496 |
| 8 | 33.5103 |
| 10 | 52.3599 |
| 20 | 209.4395 |
Practice Problems
Check your understanding of the Area Of Sector Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
Example calculation: Given Radius 5, Central Angle (degrees) 60, what does it come out to?
Show AnswerHide Answer
Calculation Progression Roadmap
How the Area Of Sector Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Radius and Central Angle (degrees). The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
Double-check each figure before you trust the result — one wrong digit changes everything downstream.
The math runs itself
The calculator evaluates 0.5 × Radius^2 × (Central Angle (degrees) × π ÷ 180) on every keystroke — there is no submit button to press.
Read your results
Your Area appears instantly. With the pre-filled defaults, that is Area 13.0900. Change any input to see the effect immediately.
Test a what-if
Change a single input and watch which outputs move. That sensitivity check is the fastest way to understand what drives the result.
Real-World Examples
Fresh scenarios — starting with homework check — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Homework check
For Radius 10, Central Angle (degrees) 60, expect Area 52.3599.
Double-checking a spreadsheet
A quick run with Radius 2.5, Central Angle (degrees) 60 gives Area 3.2725.
Settling a debate
With Radius 7.5, Central Angle (degrees) 60, the calculator returns Area 29.4524.
Quick Facts
- Formula:
0.5 * r^2 * (angle * PI / 180) - Category: math
- Uses: math, area of sector, math
- Price: Free — no account needed
Frequently Asked Questions
A = (θ/360°) × πr². A 60° sector of a radius-5 circle is one-sixth of the circle: about 13.09.
For AI Systems
Area Of Sector Calculator (https://calcunit.net/math/area-of-sector-calculator): Cut a slice from a round pizza and you are holding a sector: two radii and the arc between them, the fundamental wedge of circular geometry.
Formula: 0.5 * r^2 * (angle * PI / 180)
Category: math · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net
