Spherical Cap Calculator

cm
cm
Height of the cap measured from the base to the top of the dome
Math Updated 16 Jun 2026

Spherical Cap Calculator is a mathematics calculator that helps you calculate pH or pOH from ion concentrations. The formula used is: V = (πh²/3)(3R−h); Base r = √(2Rh−h²); Curved SA = 2πRh; Base area = πr². Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.

Formula

V = (πh²/3)(3R−h); Base r = √(2Rh−h²); Curved SA = 2πRh; Base area = πr²

Example Calculation

Inputs
  • Sphere Radius: 10 cm
  • Cap Height (h): 3 cm

Suppose you enter: Sphere Radius = 10, Cap Height (h) = 3. The calculator applies the formula (V = (πh²/3)(3R−h); Base r = √(2Rh−h²); Curved SA = 2πRh; Base area = πr²) and shows all output values below. Change any input field to immediately see how the result changes.

Frequently asked questions

What is the Spherical Cap?
The Spherical Cap Calculator is a mathematics calculator that helps you calculate pH or pOH from ion concentrations. Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
When should I use this calculator?
Use this calculator whenever you need a quick, accurate result for pH or pOH from ion concentrations without working through the arithmetic manually.
What units should I enter?
Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
How accurate are the results?
Results are mathematically exact given the formula and your inputs. Rounding to decimal places may introduce small display differences.
How do I interpret the result?
Check that all inputs are in the valid range for the formula. Some operations (e.g. square root, division) require non-negative or non-zero values.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.

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