Solve every property of a circle from any one input - radius, diameter, circumference or area. Useful for geometry homework, pipe sizing, wheel measurements and graphic design.
Radius
5
Diameter
10
2 × radius
Circumference
31.4159
2πr
Area
78.5398
πr²
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The circle is one of the most fundamental geometric shapes - defined by a single parameter (the radius) yet producing four distinct measurable quantities: diameter, circumference, area and curvature. Every circular object you encounter - coins, plates, wheels, pipes, drainage manholes, running tracks, pizza, clock faces - uses these same four properties. Master one input and you can derive everything else with just π and basic algebra.
This calculator works in any direction: enter whichever value you know (radius, diameter, circumference or area) and the other three appear instantly with their formulas. For students learning Class 6-10 geometry, it's a homework verifier. For engineers, plumbers and metal workers, it converts between pipe sizing standards (where outer diameter is the spec but cross-sectional area determines flow rate). For graphic designers and crafters, it converts between visual diameter and the area or perimeter they need to cover.
Pick what you know: radius, diameter, circumference, or area.
Enter the value.
See all four properties at once.
Once you have the radius, every other property follows directly: diameter = 2r, circumference = 2πr, area = πr². Working backwards from any of these gives the same radius.
Diameter = 2r Circumference = 2πr = πd Area = πr²
The circle's properties all derive from a single parameter - the radius r. Diameter d = 2r (the longest chord, passing through the centre). Circumference C = 2πr = πd (the perimeter, found by 'unrolling' the circle into a line). Area A = πr² (derived in calculus by integrating thin concentric rings or by limits of inscribed polygons).
The constant π ≈ 3.14159265... is irrational (no exact fraction) and transcendental (no polynomial roots). It's the ratio of circumference to diameter, identical for every circle regardless of size. Most engineering and everyday calculations use π ≈ 3.14159 (6 significant figures) which is accurate to better than 1 part per million - far more than any physical measurement of a real circle requires.
Working backwards: if you know circumference and need the radius, r = C/(2π). If you know area, r = √(A/π). The calculator handles all four directions seamlessly. For practical use, remember the proportional relationships: doubling the radius doubles the circumference but quadruples the area. Tripling the radius triples C but increases A by 9×. This explains why a 16-inch pizza has 78% more area (not 33% more) than a 12-inch one - area scales with radius squared.
12-inch pizza (diameter): r = 6 inches, A = π × 36 ≈ 113 in². 16-inch pizza: r = 8 inches, A = π × 64 ≈ 201 in². The 16-inch has 78% more pizza than the 12-inch, despite costing typically only 25-40% more. This is why ordering larger pizzas is almost always more cost-effective per square inch.
Diameter 26 inches → C = π × 26 ≈ 81.68 inches per revolution = 2.075 meters per turn. If you ride 5 km, that's 5000/2.075 ≈ 2410 revolutions of the wheel. Used for cycle computers that count wheel turns to estimate distance.
Inner diameter ≈ 6.065 inches → inner radius ≈ 3.033 inches → cross-sectional area = π × 3.033² ≈ 28.89 in². Determines water flow rate - area × velocity = volumetric flow.
π is the ratio of any circle's circumference to its diameter - irrational and approximately 3.14159265… It has infinite non-repeating decimal places.
Diameter goes all the way across; radius is half of that. Diameter = 2 × radius.
Rearrange A = πr²: r = √(A / π). For circumference: r = C / (2π).
Both ultimately measure how curved space behaves. The area formula can be derived by integrating circumference (as a circle of radius r is built up from concentric rings of radius 0 to r).
Pipe cross-section area (for flow rate), wheel circumference (for distance per revolution), sector areas (pizza slices), running tracks (lap distance).
An arc is a portion of the circumference; a sector is a pie-slice (two radii + an arc). Their lengths/areas are proportional to the angle they cover (out of 360°).
From simple percentages to scientific notation, statistics, geometry and big-number arithmetic - every common math problem you'd reach for a calculator for, runs in your browser with no installs. The fraction calculator preserves exact rationals, the big-number calculator uses BigInt for hundreds of digits without precision loss, and the scientific calculator's expression evaluator is a hand-written shunting-yard parser (no eval) that supports trig, log, factorial and parentheses.
If you're a student, double-check your work without paying for a graphing calculator. If you're a professional, use these tools as a sanity check on spreadsheet formulas. Every result is shown alongside its formula and inputs, so the math is always auditable.
The Circle Calculator is part of the Math suite on Online Calculator Tools, alongside 6 related calculators. All tools share the same UI patterns, the same privacy-first rendering (nothing is sent to a server), and the same commitment to showing the formula and assumptions behind every result.
