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03 // Bidirectional STEM Calculators // MATHA = (θ / 360) × π × r²

Circle & Circular Sector Area, Radius & Angle Solver

The area A of a circle or circular sector is proportional to the central sweep angle θ (360° for a complete circle) and the square of its radius r: A = (θ / 360) × π × r².

A = (θ / 360) × π × r²
Pick which value you want to calculate (or type into any field):Solving for: A — Circle / Sector Area
Calculated

Enclosed surface area in square units

0.011,000,000.00

Distance from center to perimeter

0.0110,000.00

360° for a full circle, 180° for semicircle, 90° for quadrant

1360
deg
Calculated Result · Circle / Sector Area (A)
314.1593m²
Converted units:

Step-by-Step Calculation

01Canonical Law: A = (θ / 360) × π × r²
02Given Inputs (Base Units): r = 10 m, θ (°) = 360
03Solve for A (Circle / Sector Area): A = 314.16 m²

The area A of a circle or circular sector is proportional to the central sweep angle θ (360° for a complete circle) and the square of its radius r: A = (θ / 360) × π × r².

Real-World Reference Values

Full Circle (θ = 360°)A = π r² | C = 2π r

Circumference at r = 10 is 62.8319

Semicircle (θ = 180°)A = ½ π r²

Half-disc cross-section

Arc Length Formulas = (θ / 360) × 2π r = 2A / r

Boundary arc length equals 2A / r

20-Row Comparison Table

Circle / Sector Area (A) · Radius (r)

Circle & Circular Sector Area, Radius & Angle Solver — Radius → Circle / Sector Area
#Radius (m)Circle / Sector Area (m²)Δ %
0110 mCurrent314.1593 m²0.00%
0272.9041 m16,697.61 m²+5215.01%
03145.7983 m66,781.27 m²+21157.14%
04218.6924 m150,250.98 m²+47726.37%
05291.5866 m267,106.75 m²+84922.72%
06364.4807 m417,348.56 m²+132746.17%
07437.3748 m600,976.44 m²+191196.74%
08510.269 m817,990.36 m²+260274.42%
09583.1631 m1,068,390.34 m²+339979.21%
10656.0572 m1,352,176.37 m²+430311.11%
11728.9514 m1,669,348.45 m²+531270.12%
12801.8455 m2,019,906.59 m²+642856.24%
13874.7397 m2,403,850.78 m²+765069.47%
14947.6338 m2,821,181.03 m²+897909.81%
151,020.53 m3,271,897.32 m²+1041377.26%
161,093.42 m3,755,999.67 m²+1195471.83%
171,166.32 m4,273,488.08 m²+1360193.50%
181,239.21 m4,824,362.53 m²+1535542.29%
191,312.10 m5,408,623.04 m²+1721518.18%
201,385.00 m6,026,269.60 m²+1918121.19%
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Frequently Asked Questions

How do I solve for the radius of a full circle from its area?+

Keep θ = 360°, click SOLVE FOR on r (Radius), and enter your circle's area A to evaluate r = √(A / π).

How is circumference C related to area A?+

For a full circle, Circumference C = 2πr = 2 × √(π × A) = 2A / r.

What is 1 radian in degrees?+

One radian is the central angle where arc length equals radius: 180° / π ≈ 57.2958°.