Calculate the radius of a circle from the diameter, circumference, area, arc length, or sector area. Instant results with all circle properties, visual bars, and a reference table.
The radius of a circle is the distance from the center point to any point on the circumference. It is one of the most fundamental measurements in geometry, forming the basis for nearly every circle-related formula. Whether you are designing a circular garden, sizing a pipe, or solving a math homework problem, knowing how to find the radius quickly and accurately is essential.
This calculator lets you determine the radius of a circle using five different starting measurements: diameter, circumference, area, arc length with a central angle, or sector area with a central angle. Simply choose your solve method, enter the known value, and the tool instantly computes the radius along with all other key circle properties — diameter, circumference, area, a 90-degree arc length, and the corresponding sector area.
The relationship between the radius and other circle dimensions is governed by the constant π (pi ≈ 3.14159). The diameter is always exactly twice the radius. The circumference equals 2πr, and the area equals πr². For arc-based calculations, the formulas incorporate the central angle in degrees, giving you flexibility when working with partial circles, sectors, or arc segments.
Use the built-in presets for common real-world objects like coins, pizzas, tires, and trampolines to explore results instantly. The reference table of common circle sizes provides a handy lookup for everyday comparisons. Visual proportion bars help you see how the radius and diameter relate at a glance.
Radius is the measurement that unlocks nearly every other circle formula, but in real problems it is often the one value you do not start with. You may measure the diameter of a lid, the circumference of a wheel, the area of a circular pad, or the arc data from a drawing. This calculator converts those different inputs into radius immediately and then rebuilds the other circle properties from the result.
That makes it useful far beyond basic geometry homework. It helps with fabrication, estimating, drafting, product sizing, and any workflow where circular parts are described in mixed ways across drawings, labels, or field measurements.
r = d/2 | r = C/(2π) | r = √(A/π) | r = L/(θ·π/180) | r = √(2S/(θ·π/180)), where d = diameter, C = circumference, A = area, L = arc length, S = sector area, θ = central angle in degrees.
Result: Radius = 5.0003 cm, diameter = 10.0006 cm, area = 78.5482 cm².
Using mode = circumference with value1 = 31.42 cm, the calculator applies r = C / (2π). That gives a radius of about 5.0003 cm, which is essentially 5 cm at normal classroom precision. From that radius it also derives the diameter, circumference check, full area, 90-degree arc length, and 90-degree sector area.
Once you know the radius of a circle, every other standard circle measurement follows immediately. Diameter is 2r, circumference is 2πr, and area is πr². That is why so many geometry and engineering problems reduce to finding radius first, even when the original problem statement never mentions it directly.
This calculator is built around that idea. No matter which solve method you choose, the workflow is the same: recover the radius, then derive the rest of the circle from that one value.', + '
Use diameter mode when you can measure straight across a circular object through its center. Use circumference mode when you can wrap a tape or string around the edge. Use area mode when the circular region is known from plans or calculations. Arc and sector modes are most useful when you are working with only part of a circle and you also know the central angle.
Those options match how circle data is actually encountered in practice. A pipe might be labeled by diameter, a wheel can be checked by circumference, and a CAD sketch may specify an arc length plus angle rather than a full circle size.', + '
A lot of mistakes happen because people switch between diameter, radius, circumference, and area without pausing to convert carefully. Doubling when you should divide, forgetting π, or mixing degrees with radians can all produce answers that look plausible but are wrong. A multi-method radius tool helps prevent that by keeping the formulas tied to the correct input context.
It also gives you a quick way to sanity-check measurements. If the derived radius makes the diameter, circumference, or area look unreasonable for the real object, you know something in the original measurement or unit choice needs another look.
The radius is the distance from the exact center of a circle to any point on its edge (circumference). It is half the diameter and is used in nearly all circle calculations.
Divide the circumference by 2π (approximately 6.2832). For example, a circumference of 31.42 cm gives a radius of about 5 cm.
Divide the area by π and then take the square root: r = √(A/π). For example, an area of 78.54 cm² gives a radius of about 5 cm.
The diameter is the full distance across a circle through its center, while the radius is half that distance. Diameter = 2 × radius.
Yes, if you also know the central angle. The formula is r = arc length / (angle in radians). This calculator converts degrees to radians automatically.
Pi is the ratio of a circle's circumference to its diameter. It appears in every formula relating the radius to circumference, area, arcs, and sectors because circles are fundamentally defined by this constant.