Diameter, circumference and area
From a circle's radius you can find everything else: the diameter is 2 × r, the circumference is 2 × π × r, and the area is π × r². For a radius of 5: diameter 10, circumference about 31.42, and area about 78.54.
The three results come from a single measurement because a circle has only one degree of freedom — fix the radius and the shape is completely determined. Note how the units differ: the diameter and circumference are plain lengths, while the area is in square units. Doubling the radius the other way gives the distance around the rim, which the circle circumference calculator handles.
How to use this calculator
Enter the radius — the distance from the center to the edge. The result shows the diameter, circumference, and area together. If you started from the diameter, the radius is just half of it.
Mixing up radius and diameter is by far the most common error. Measuring across the widest part of a circular object gives the diameter, so halve it before entering. Entering a diameter of 10 as if it were the radius would report an area of about 314 instead of 78.54 — four times too large.
Working backward
Have the circumference instead? The radius is C ÷ (2π). Have the area? The radius is √(A ÷ π). For the area alone, the area of a circle calculator focuses on that; for a slice of the edge, the arc length calculator.
These rearrangements come straight from the forward formulas. Checking with the numbers above: 31.42 ÷ (2π) ≈ 5 and √(78.54 ÷ π) ≈ 5, a quick way to confirm a measurement you are unsure about.
Frequently asked questions
- How do I find the diameter from the radius?
- Multiply the radius by 2. A radius of 5 gives a diameter of 10.
- What is the circumference of a circle?
- Circumference = 2 × π × r. For a radius of 5 it's about 31.42.
- How do I find the radius from the circumference?
- Divide the circumference by 2π. For a circumference of 31.42, the radius is about 5.
- What is the area of the circle with radius 5?
- About 78.54 square units (π × 25).
- What happens to the area if I double the diameter?
- The area becomes four times larger, not twice. Area depends on the radius squared, so doubling the size multiplies the area by 2² = 4, while the circumference only doubles.