Circle Calculator
Full Circle Solver, Plus Arc & Sector
Give this tool any one known circle value and it derives all the others, plus a bonus arc length and sector area solver. This has much more depth than the Area Calculator's circle mode, which is intentionally just a single quick π × r² formula.
Solve From Any Known Value
Bonus: Arc Length & Sector Area
Given a radius and a central angle (in degrees), find the length of the arc and the area of that "pie slice" sector.
Understanding Circle Geometry
A circle's radius, diameter, circumference, and area are all tightly linked — knowing just one of them is enough to find the rest. This calculator goes well beyond the Area Calculator's single-formula circle mode, offering a full four-value breakdown from any starting point, plus arc length and sector area for partial circles.
Whether you know the radius, diameter, circumference, or area, the calculator solves for the radius first, then derives the other three — no need to remember which formula to rearrange.
Beyond the whole circle, the bonus tool finds the arc length and sector area for any "pie slice" defined by a central angle between 0° and 360°.
The Formulas
Diameter
Circumference
Area
Radius From Area
Arc Length
Sector Area
In the arc and sector formulas, θ is the central angle in degrees; multiplying by π/180 converts it to radians.
Deeper Than a Quick Area Formula, By Design
The Area Calculator deliberately keeps its circle mode to one formula (π × r²) because it's built for speed across seven different shapes. This Circle Calculator is the opposite: it's dedicated entirely to circles, so it can afford to solve from any known starting value and cover partial-circle geometry like arcs and sectors — depth that a general multi-shape tool intentionally leaves out.
Radius, diameter, circumference, and area — from any one starting value.
A sector's central angle must be greater than 0° and no more than a full circle.
Every circle formula on this page relies on the ratio of circumference to diameter, π.
Key Takeaways
- Any one of radius, diameter, circumference, or area is enough to derive all the others.
- Arc length and sector area extend the same formulas to a "slice" of the circle defined by a central angle.
- Just need a quick area? The Area Calculator's single-formula circle mode is faster if you don't need the full breakdown.
Frequently Asked Questions
- In the first section, choose which value you already know — radius, diameter, circumference, or area — and enter it.
- Click "Calculate" to instantly see all four circle measurements.
- Optionally, use the second section to find the arc length and sector area for a given radius and central angle (in degrees).
The Area Calculator intentionally offers just one simple circle formula (π × r²) for a quick answer. This Circle Calculator goes much deeper: give it any one of radius, diameter, circumference, or area, and it derives all the others — plus it solves arc length and sector area for a given central angle, which the Area Calculator doesn't do at all.
That's exactly what this tool is built for. Enter whichever one value you know — radius, diameter, circumference, or area — and select the matching option from the dropdown. The calculator solves for the radius first (using r = d/2, r = C/(2π), or r = √(A/π) depending on what you gave it), then derives the remaining three values from that radius.
A sector is a "pie slice" of a circle bounded by two radii and the arc between them, defined by a central angle. Sector area is a fraction of the full circle's area, proportional to how much of the full 360° the central angle covers — a 90° sector, for example, covers exactly one quarter of the circle's total area.
A central angle of 0° describes no arc at all, and any value beyond 360° would simply wrap back around the circle more than once, which isn't a meaningful "slice" for a single arc length or sector area calculation. A full 360° angle is valid and simply returns the entire circumference and the entire circle's area.
Yes — if all you need is a quick π × r² area calculation without the diameter/circumference breakdown or the arc/sector tools, the Area Calculator's circle mode is faster for that single purpose.