Circle Calculator

The circle calculator derives the remaining three properties of a circle, radius, diameter, circumference, and area, from any single one of them. It accepts decimals, fractions such as 3/4, and mixed numbers such as 5 1/16 on the input side, so a ruler reading in sixteenths or a metric spec sheet in millimeters both parse without manual conversion first.

The core formulas:

• Diameter: D = 2r
• Radius: r = D/2 = C/(2π) = √(A/π)
• Circumference: C = 2πr = πD
• Area: A = πr² = π(D/2)² = π(C/(2π))²

Reading and adjusting the result:

• Only one known value is required, radius, diameter, circumference, or area, in decimal or fraction form (for example, 5 mm, 5 1/16 in, 0.75 ft, or 22/7 in). Area is entered in a square unit.
• An output unit converts every result at once: a radius of 5 mm with the output unit set to inch returns the radius as roughly 0.19685 in, with diameter, circumference, and area converted to inches and inches² in the same step.
• Fraction precision gives carpenter-style output (0.19685 in reads as roughly 13/64 in); decimal precision suits technical tolerances instead.
• π defaults to its exact value but can be swapped for the common approximations 22/7 or 355/113, or a custom value, to mirror a classroom convention or a design requirement.
• A minimal step-by-step derivation can be shown for each result, useful for checking how a value was reached rather than only reading the answer.

Because input is fraction-or-decimal agnostic, a mixed number such as 5 1/16 entered as inches converts to a different output unit, such as centimeters, from that single entry, with no retyping or manual conversion of the original figure. That is what removes the back-and-forth unit math from the workflow.

Circle measurements, conversions, and quick checks come up in geometry practice, shop-floor planning, and cross-unit comparisons alike, all served by the same formulas and flexible inputs.

• Classroom and homework: Checking an assignment means entering any given value and confirming the remaining properties against the standard formulas; setting π to 22/7 matches typical textbook convention.
• Woodworking and fabrication: A fractional measurement such as 5 1/16 in for a circular template converts to millimeters for CNC or metric toolpaths, with fraction precision presenting cut sizes in 1/16 in or 1/32 in.
• 3D printing and CAD: A metric spec such as 5 mm diameter converts to inches for a mixed-standard project, with decimal precision matched to the model's tolerances.
• Machining and QA: Circumference or area can be verified from a single gauge reading; a custom π value reproduces legacy calculations from established shop notes.
• STEM labs and demonstrations: Changing one variable shows how all the others respond, with step-by-step mode displaying each derivation for teaching or lab reports.
• Hobby projects: Circular art pieces, leathercraft, lenses, and wheels can be planned from one convenient measurement, then converted to a preferred unit system without hand calculation.

The output unit performs fast cross-unit conversion from a single entry: 5 mm entered as diameter, with the output unit set to inch, gives diameter, circumference, and area in inches and inches²; entering 5 1/16 as diameter in inches gives the equivalent metric results without manual conversion. That single workflow cuts a common source of error in education, design, and production work.