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Sector Calculator | Compute Area From Radius and Radian Angle

Calculate the area, arc length, chord length and perimeter of any circle sector from the radius and angle, in degrees or radians. Essential for pie portions, gear segments, irrigation coverage and circular statistics.

Last updated: June 2026 · Free · No sign-up required

deg
Results

Enter values above and click Calculate to see your result instantly.

How the Sector Calculator works

Under the hood, this calculator applies Area = ½ r² θ (θ in radians); arc = rθ; chord = 2r sin(θ/2), so the sector area calculator result you see is genuine math, not a lookup table.

The reference table below covers the most common sector area calculator cases at a glance, the methodology section breaks the calculation into verifiable steps, and the FAQ tackles the edge cases.

Quick reference

RadiusAngleAreaArc length
560°13.095.24
590°19.637.85
1045°39.277.85
8120°67.0216.76

info Sector Calculator

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

OutputFormula
Sector area½r²θ = (θ/360)×πr²
Arc lengthrθ (θ in radians)
Chord2r·sin(θ/2)
Perimeterarc + 2r

lightbulb Worked example

Let's say you are using the Sector Calculator. Calculates sector area using Area = ½ r² θ (θ in radians), in real time in your browser. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula Area = ½ r² θ (θ in radians); arc = rθ; chord = 2r sin(θ/2) and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: Area = ½ r² θ (θ in radians); arc = rθ; chord = 2r sin(θ/2)

How the sector measurements are calculated

The tool applies Area = ½r²θ with θ in radians, arc length = rθ, chord length = 2r sin(θ/2), and perimeter = arc + 2r. Angles entered in degrees are converted to radians automatically, and every formula is displayed with the working.

Example: a 60° sector of a circle with radius 6 has area ½ × 36 × (π/3) ≈ 18.85 square units and arc length 6 × (π/3) ≈ 6.28 units.

Reading the result: the sector is the circular slice — pizza portions, gear segments, irrigation coverage, and radar sweeps all use these formulas. The area gives material estimates, the arc gives the curved boundary length for fencing or cutting, and the chord is the straight-line distance across the slice.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do you find the area of a sector?
Enter the required values into the input fields and press the calculate button. The tool applies the formula Area = ½ r² θ (θ in radians); arc = rθ; chord = 2r sin(θ/2) and returns the result with a short explanation of each step, so you can check the working yourself.
What is arc length and how is it different from the chord?
The Sector Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Calculates sector area using Area = ½ r² θ (θ in radians), in real time in your browser. There is no limit on usage, and it works on any device.
What is the sector perimeter?
The perimeter of a sector is the sum of its arc length and the two radii: P = rθ + 2r (with θ in radians). For a 60° sector of radius 6, the arc is about 6.28 units and the perimeter about 18.28 units. The calculator returns the arc length, chord length, and perimeter alongside the area, covering every linear measure of the sector.
Does the calculator accept radians?
Yes — you can enter the angle in degrees or radians, and the tool converts internally since the area formula Area = ½r²θ requires radians. A 60° angle becomes π/3 radians automatically. The results are consistent either way, and the working shows the conversion so you can verify the arithmetic.
What real-world problems use sectors?
Sectors describe circular slices: pie and pizza portions, gear segments, irrigation coverage, radar and sonar sweeps, and circular statistics. The area formula ½r²θ sizes anything from a slice of cake to the coverage of a rotating sprinkler. The chord and arc measures matter for cutting materials, fencing curved boundaries, and layout work.
What does the Sector Calculator do?
Calculates sector area using Area = ½ r² θ (θ in radians), in real time in your browser. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Sector Calculator use?
It uses Area = ½ r² θ with the angle θ in radians, the arc length = rθ, and the chord length = 2r sin(θ/2). Enter the radius and the sector angle, and the tool returns the area, arc length, and chord. For a 60° sector of a circle with radius 6, the area is about 18.85 square units.
Is the Sector Calculator free and private?
Yes — the Sector Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Sector Calculator?
The Sector Calculator applies the standard formula: Area = ½ r² θ (θ in radians); arc = rθ; chord = 2r sin(θ/2). It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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