Volume Of Hemisphere Calculator - Half-Sphere Volume, Curved Area, and Total Area

A volume of hemisphere calculator turns the radius, diameter, or circumference of a half-sphere into its enclosed volume in real time, with a length-unit selector for the linear input and a separate capacity-unit selector for the volume readout.

• • Bowls, domes, and skylights: Designers of glass domes, half-sphere skylights, and decorative bowls read off the fill volume in liters and US gallons without re-entering numbers.
• • Tanks and pressure vessels: Engineers sizing half-sphere tank ends and spherical pressure-vessel heads get the exact interior capacity and surface area for material estimates.
• • Cooking and recipe scaling: Bakers scaling a half-sphere mousse or a hemisphere cake pan convert the diameter into batter or dough volume.
• • Geometry homework and exams: Students working through integration problems get the closed-form answer with side-by-side unit readouts for cross-checks.

A hemisphere is the half of a sphere cut by a plane through the center, so the same three numbers describe it as a sphere: a radius r, a diameter d = 2r, and a great-circle circumference c = 2πr. The hemisphere has a curved outer surface and a flat circular base of radius r, and the volume inside the curved surface is exactly half the volume of a full sphere. Pick a length unit for the input, a capacity unit for the readout, and the calculator returns the volume, the curved area, the base area, and the total area in one pass.

A hemisphere is exactly half of a full sphere, so it helps to keep the Sphere Volume Calculator nearby for the V = (4/3)πr³ base case and the r ↔ d ↔ c conversions.

The calculator applies V = (2/3)πr³, derives curved surface area A_curved = 2πr² and total surface area A_total = 3πr², and reports the radius and the equivalent sphere volume for context. The input is first normalized to a radius in centimeters, then the chosen capacity unit is applied to the resulting volume with an exact factor.

• r: The radius of the hemisphere in the chosen length unit. The calculator converts to centimeters before applying V = (2/3)πr³, then labels the radius and area readouts in the chosen unit.
• Input type: Radius, diameter, or circumference. For diameter the radius is r = d / 2 and for circumference the radius is r = c / (2π).
• Length unit: Cm, m, in, or ft. The calculator converts to centimeters before applying the formula, then labels the radius and surface-area readouts in the chosen unit.
• Volume unit: Cm³, m³, in³, ft³, L, or US gal. The chosen unit is applied to the internally computed cubic-centimeter volume with an exact factor.

The formula comes from cutting a sphere in half. A full sphere has volume V_sphere = (4/3)πr³, and a hemisphere is exactly half of a sphere cut by a plane through the center, so V_hemisphere = (1/2) · (4/3)πr³ = (2/3)πr³. The curved surface area is also half of a full sphere's, so A_curved = (1/2) · 4πr² = 2πr². Add the flat circular base πr² to get the total surface area 3πr², which is what you would measure for a closed dome with a circular rim.

According to Wolfram MathWorld, a hemisphere is exactly half of a sphere cut by a plane through the center, so its volume is V = (1/2) · (4/3)πr³ = (2/3)πr³.

When you want to size the flat circular base of the hemisphere separately, the Circle Calculator gives you radius, diameter, circumference, and disk area from the same input.

These four ideas are enough to read every hemisphere volume formula you will meet in a textbook, a CAD package, or a calculator like this one:

A useful intuition is to think of a hemisphere as a full sphere with one flat face glued on. The curved area is half the sphere, the flat face is a disk of area πr², and the closed dome has total area 3πr². Memorize the volume V = (2/3)πr³ and the rest follows.

When a tapered or pointed shape fits the design better than a dome, the Cone Volume Calculator handles the related (1/3)πr²h case with the same base radius.

Four short steps take you from one raw measurement to a complete hemisphere capacity readout:

1. 1 Pick the input type: Choose Radius, Diameter, or Circumference depending on which measurement is easiest to read off the object in front of you.
2. 2 Enter the measurement value: Type the value in the chosen length unit. The calculator normalizes to a radius automatically before applying the hemisphere formula.
3. 3 Pick the length unit and a capacity unit: Choose cm, m, in, or ft for the input, then choose cm³, m³, in³, ft³, L, or US gal for the primary volume readout.
4. 4 Read the result panel: The primary hemisphere volume, side-by-side capacity readouts, the calculated radius, and the curved and total surface areas all update as you type.

For a glass dome with diameter 30 cm, the calculator reports about 7,069 cm³ of interior volume (7.07 L, 1.87 US gal) with cm chosen as the length unit, plus a curved area of about 1,414 cm² and a total surface area of about 2,121 cm² for the closed dome.

If you need the same interior volume in a unit that is not on the dropdown, the Volume Converter extends the result to teaspoons, tablespoons, cups, quarts, and many more capacity units.

Why reach for an online volume of hemisphere calculator instead of working the formula by hand each time?

• • Accepts radius, diameter, or circumference: Type whichever measurement is easiest to read off the object and the calculator normalizes to a radius automatically.
• • Capacity units side by side: Shows the same interior volume in cm³, m³, in³, ft³, L, and US gal at once for engineering specs, cooking, and fluid estimates.
• • Pairs volume with area readouts: Reports the curved area, the circular base, and the closed-dome total area alongside the volume so you can size a lining, a coating, or a glass dome.
• • Cross-checks against a full sphere: Shows the equivalent sphere volume at the same radius so you can confirm that the hemisphere is exactly half of it.
• • Length and capacity units stay independent: Pick cm, m, in, or ft for the linear input and cm³, m³, in³, ft³, L, or US gal for the volume output, all without re-entering values.

Type a new diameter, switch the length unit from cm to in, and watch the radius and area readouts re-label, then switch the volume unit to US gal and watch the capacity readout change.

Archimedes showed that a hemisphere is exactly two-thirds the volume of its circumscribing cylinder, and the Cylinder Volume Calculator lets you confirm that relationship for the same radius and height.

The hemisphere volume formula looks short, but the four factors below decide whether the answer matches the half-sphere in front of you:

• • The hemisphere volume formula assumes a perfect half-sphere with the flat face perpendicular to the curved surface. A partial dome (less than a hemisphere) or a shape with an elliptical base will not match the closed-form answer.
• • The volume returned is geometric. Real bowls, domes, and tanks have wall thickness, surface curvature imperfections, and interior fittings that change the true fill volume, so do not size a fluid tank without an extra safety margin.

According to Wikipedia, the volume of a hemisphere is V = (2/3)πr³ and its curved surface area is 2πr², while the total surface area including the flat circular base is 3πr².

According to Encyclopaedia Britannica, Archimedes proved that a sphere (and therefore a hemisphere) is exactly two-thirds the volume of the cylinder (or half-cylinder) that just contains it, which gives the closed-form volume V = (2/3)πr³ for any hemisphere.

For the flat circular base or any 2D reference area in the same design, the Area Calculator gives the surface measurement without leaving the page.