Circle Formulas
Learn the circle formulas for diameter, circumference, area, arc length, sector area, chord length, and the equation of a circle.
These formulas connect a circle’s radius to its boundary, area, arcs, sectors, chords, and position on the coordinate plane.
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7 formulas, different jobs
These formulas connect a circle’s radius to its boundary, area, arcs, sectors, chords, and position on the coordinate plane.
Radius and Diameter
Use it to switch between the radius and full width of a circle.
Circumference
Use it to find the distance around a circle.
Area of a Circle
Use it to find the region enclosed by the circle.
Arc Length
Use it for the curved length cut out by a central angle in degrees.
Sector Area
Use it to find the area of a slice of a circle.
Chord Length
Use it when the radius and the chord’s central angle are known.
Standard Equation of a Circle
Use it for a circle centered at (h, k) on the coordinate plane.
One circle, seven connected results
Use a circle with radius 6, central angle 60°, and center (2, −1) to connect its main measurements and equation.
- 1 · Whole circle
- 2 · Arc
- 3 · Sector and chord
- 4 · Equation
Common mistakes
- Using the diameter where a formula requires the radius.
- Forgetting to square the radius in the area formula.
- Using degree-based arc or sector formulas with an angle measured in radians.
See which formulas your problem uses
Enter a problem and get a step-by-step solution with the formulas and theorems identified.
Calculators and related formula guides
Geometry Calculator
Solve circle and shape measurement problems.
Equation Calculator
Rearrange circle formulas and solve for unknown values.
Slope formulas
Compare the slope formula, point-slope form, slope-intercept form, standard form, and special horizontal and vertical lines.
Quadratic equations
Learn the essential quadratic equation formulas for solving, checking roots, and graphing a parabola, with one connected example.
Circle formulas FAQ
Should I use radius or diameter in a circle formula?
Area, arc, sector, chord, and circle-equation formulas use the radius. Circumference can use either C = 2πr or C = πd.
Do arc-length formulas use degrees or radians?
The fraction θ/360 uses degrees. With radians, use L = rθ instead.