Circle Calculator
Enter a circle's radius, diameter, circumference, or area and get all the others, plus π and the exact relationships between them.
كيفية استخدام هذه الحاسبة
- 1Choose which measurement you already know — radius, diameter, circumference, or area.
- 2Enter its value.
- 3Read the radius, diameter, circumference, and area of the circle.
- 4See the area expressed as a multiple of π for an exact form.
طريقة الحساب
Circle measurements
diameter = 2 × radius circumference = 2π × radius = π × diameter area = π × radius² radius = √(area ÷ π) = circumference ÷ 2π
A circle is defined entirely by a single measurement — its radius, the distance from the centre to the edge — and every other quantity follows from it through the constant π. The diameter is just twice the radius, spanning the circle through its centre. The circumference, the distance around the circle, is π times the diameter, or equivalently 2π times the radius; this is the very definition of π, the ratio of any circle's circumference to its diameter. The area enclosed is π times the radius squared. Because all four quantities are linked, knowing any one lets you work back to the radius and then forward to all the rest, which is what this calculator does. The one relationship worth internalising is that area depends on the square of the radius, so it grows much faster than the radius itself.
مثال محلول
A circle with a radius of 5 has a diameter of 10, a circumference of 2π × 5 ≈ 31.42, and an area of π × 5² ≈ 78.54. If instead you knew only the area was 78.54, you could recover the radius as √(78.54 ÷ π) = 5 and rebuild every other measurement from there.
Circle Calculator: الدليل الكامل
π: the constant that ties a circle together
Every measurement of a circle is connected through a single constant, π (pi), which is the ratio of a circle's circumference to its diameter. This ratio is exactly the same for every circle, from a coin to a planet's orbit — roughly 3.14159, though its decimal expansion never ends or repeats, making π an irrational number. That universality is what makes the circle formulas so clean: because circumference divided by diameter is always π, the circumference must be π times the diameter, and everything else cascades from there.
This is why knowing any one measurement of a circle is enough to find all the others. The radius, diameter, circumference, and area are not four independent facts but four faces of the same thing, locked together by π. Working from the radius is usually easiest, since the diameter, circumference, and area are all simple expressions in it, but the relationships run both ways — given the area or circumference, you can just as well work back to the radius and out again to whatever you need.
Why area grows with the square of the radius
The most important and most frequently misjudged fact about circles is that area depends on the square of the radius, not the radius itself. Doubling the radius does not double the area — it quadruples it, because the area is proportional to r². Tripling the radius makes the area nine times larger. This non-linear growth is deeply unintuitive, and it trips people up constantly when reasoning about round things.
The consequences are everywhere once you look. A 16-inch pizza has not merely a bit more food than a 12-inch one; it has nearly twice the area, and usually far better value per square inch, even though the diameters differ by only a third. A pipe of twice the diameter carries four times the flow. A telescope with twice the aperture gathers four times the light. Whenever a quantity depends on the area of a circular cross-section — and many physical quantities do — small increases in radius produce large increases in the result, precisely because of that squared relationship.
Circles in the world
Circles and their measurements appear throughout daily life and engineering, which is why being able to move fluently between radius, diameter, circumference, and area is such a practical skill. Buying a circular rug or table, you care about area for coverage and circumference for a border or edging. Sizing a pipe or duct, the area of the cross-section governs how much water or air can flow. Laying out a circular garden bed or patio, the area tells you how much soil, gravel, or paving to order and the circumference how much edging.
The formulas also underpin more technical work. Wheels and gears rotate through their circumference — one full turn moves a distance equal to the circumference, which is how odometers and rolling measurements work. Circular tanks and containers hold a volume based on their circular area times their height. Even the humble task of finding how much fencing rings a round enclosure, or how much fabric covers a round cushion, is a circle calculation. The circle is one of the most common shapes in the built and natural world, and this handful of π-based relationships is all it takes to measure any of them completely.
الأسئلة الشائعة
How do I find the area of a circle?
Area = π × radius². Square the radius and multiply by π (about 3.14159). A circle of radius 5 has an area of π × 25 ≈ 78.54. If you know the diameter instead, halve it first to get the radius; if you know the circumference, divide it by 2π.
What is the circumference of a circle?
The circumference is the distance around the circle, equal to 2π × radius, or equivalently π × diameter. A circle of radius 5 has a circumference of 2π × 5 ≈ 31.42. The ratio of circumference to diameter is always π, for every circle.
How do I find the radius from the area?
Divide the area by π and take the square root: radius = √(area ÷ π). For an area of 78.54, that's √(78.54 ÷ π) = √25 = 5. Once you have the radius, you can find the diameter (2 × radius) and circumference (2π × radius).
Why does doubling the radius quadruple the area?
Because area depends on the radius squared (π r²), not the radius itself. Doubling r multiplies r² by four, so the area quadruples. This is why a 16-inch pizza has nearly twice the food of a 12-inch one despite the diameters differing by only a third.