Calculators
Spherical Cap Calculator
Calculate spherical cap volume, base radius, curved surface area, and total surface area from sphere radius and cap height.
Measure a portion of a sphere cut by a plane.
A spherical cap is the part of a sphere cut off by a plane. Enter the radius R of the full sphere, not the radius of the circular base, and the perpendicular height h from the cutting plane to the cap apex. Volume V = πh²(R − h/3), base radius a = √[h(2R − h)], curved area C = 2πRh, and total area A = C + πa². For R = 5 and h = 2, volume is approximately 54.4542736622 cubic units and base radius is 4 units. Height must be between 0 and 2R: zero gives an empty cap, h = R gives a hemisphere, and h = 2R gives the whole sphere. A cap taller than R includes more than half the sphere. Total surface area includes the flat circular base; curved area excludes it. Use consistent length units. Nonzero inputs must be from 1e-50 to 1e50; results use browser floating-point arithmetic rounded to 12 significant digits. Very thin caps near the numeric precision limit may lose accuracy. This is solid geometric volume, not a hollow shell or a wall-thickness calculation. All calculations stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
Which radius should I enter?
Enter the radius of the original full sphere. The calculator finds the circular base radius from that sphere radius and the cap height.
How is cap height measured?
Measure perpendicular to the cutting plane from the plane to the cap apex. Height may range from zero to twice the sphere radius.
Does total area include the base?
Yes. Total area adds the flat circular base to the curved spherical surface.
Can I calculate a hemisphere or whole sphere?
Yes. Use height equal to the radius for a hemisphere, or twice the radius for the full sphere. Zero height gives zero volume and area.
Are my inputs uploaded?
No. Calculations run locally in your browser. Use consistent units; area is in square units and volume in cubic units.