Right Cylinder Calculator - Volume and Surface Area

A right cylinder calculator is a geometry tool that returns every standard measurement of a right circular cylinder in one pass. Enter the radius (or diameter) and the perpendicular height, and the page returns the volume, base area, lateral and total surface area, and capacity in liters and US gallons in the unit of your choice.

• • Geometry homework and textbook problems: Solve a chapter on solids of revolution: compute the volume, lateral area, and total area of a right cylinder given a base radius and a perpendicular height, including the classic π r² h and 2π r (h + r) examples.
• • Tanks, cans, and storage vessels: Estimate the liquid capacity of a vertical cylindrical tank, a hot water heater, a paint can, or a soup can, and confirm the surface area needed for insulation, paint, or wrap.

A right cylinder has its axis perpendicular to the two circular bases. An oblique cylinder leans: V = π r² h still holds, but the lateral surface area is no longer the simple 2π r h used here, so this page focuses on right circular cylinders.

For a tool that focuses on the cylinder volume formula alone with metric and imperial unit selection, the Cylinder Volume Calculator page covers the π · r² · h relationship in a stripped-down form.

The right cylinder calculator applies the standard right cylinder formulas in one pass. It takes the base dimension and the perpendicular height, converts the diameter to a radius when needed, and uses the radius and the height to compute the base area, volume, lateral and total surface areas, and the capacity in liters and US gallons.

• r: Radius of the circular base, in the chosen length unit.
• h: Perpendicular (vertical) height from the base to the top base of the cylinder.
• A_lateral: Curved side wall area, equal to 2π r h.
• A_total: Lateral area plus both circular bases, equal to 2π r (h + r).

All five geometric outputs come from the same two inputs, so the volume, base area, and surface areas are always consistent with the radius and the height you typed.

According to Wolfram MathWorld, the volume of a right cylinder of radius r and height h is V = π r^2 h, the lateral surface area is 2 π r h, and the total surface area is 2 π r (h + r)

If you only need the curved side of a right cylinder (the wrap or label area), the Lateral Surface Area Cylinder Calculator page applies 2 · π · r · h directly and skips the volume and the capacity outputs.

Four ideas explain why the right cylinder formulas look the way they do and what each result really means geometrically.

If you need a hollow cylinder (a tube), the volume is the difference between the outer and inner cylinders using the same π r² h formula on each radius.

If your real problem is a tube, a pipe, or any cylinder with a hollow core, the Hollow Cylinder Volume Calculator page subtracts the inner cylinder from the outer cylinder using the same π · r² · h formula on each radius.

Four short steps cover every common case, from a textbook example to a flat zero-height cylinder.

1. 1 Pick the base input mode: Choose 'Radius' or 'Diameter' depending on whether you know the distance from the center of the base to the rim or the full width across the base.
2. 2 Enter the base length and the perpendicular height: Type the radius (or diameter) and the vertical height in the chosen length unit. A textbook problem might use r = 3 cm, h = 10 cm; a real tank might use d = 45 cm, h = 90 cm.
3. 3 Pick the length unit: Choose centimeters, meters, inches, or feet. The volume, area, and capacity labels update to the matching cubic, squared, and linear unit, with the same volume in liters and US gallons.
4. 4 Read the results and reset: Read the volume, base area, lateral and total surface area, and capacity in liters and US gallons. Click Reset to restore the default example and start a new problem.

Try diameter = 10 cm, height = 10 cm (the same as r = 5 cm, h = 10 cm). The page shows A_base ≈ 78.5398 cm², V ≈ 785.3982 cm³, A_lateral ≈ 314.1593 cm², A_total ≈ 471.2389 cm², ≈ 0.7854 L, and ≈ 0.2075 US gallons.

A common follow-up is to compare the cylinder volume with a right circular cone of the same base and height, and the Right Circular Cone Calculator page returns the (1/3) · π · r² · h result with the same unit selection.

These benefits matter most when you are working a problem by hand and need a quick check, or when you are designing a real cylindrical object and want all the numbers in one place.

• • Six cylinder measurements in one pass: Get the volume, base area, lateral and total surface area, and capacity in liters and US gallons from the same two inputs.
• • Skips the arithmetic mistakes: Manual cylinder problems are easy to slip up on the squaring step, the 2π r h factor, or the (h + r) inside the parentheses. The page applies the formulas exactly.
• • Works for radius or diameter: Switch between radius and diameter input with a single selector, so a problem that gives you the diameter and a problem that gives you the radius both work without manual conversion.
• • Capacity in liters and US gallons: The page returns the same volume in liters and US liquid gallons using the NIST 231 in³ per gallon conversion, so a 282.74 cm³ cylinder reads as 0.2827 L and about 0.0747 US gallons without manual math.
• • Connects to the rest of the math toolkit: The page links to peer calculators for cylinder volume, lateral cylinder area, hollow cylinder volume, and right circular cone volume, so the related shapes are one click away.

Use the page to confirm a homework answer, sanity-check a tank estimate, or pre-validate a cylinder before passing it to a 3D modeling script.

If the cylinder narrows or the top is cut off to form a frustum, the Truncated Cone Volume Calculator page applies the difference of two π · r² · h cone volumes with the same metric and imperial unit selection.

The formulas in this right cylinder calculator are the same in every case, but a few factors change how the result should be read and how it is applied in a real problem.

• • This page is for right circular cylinders only. An oblique cylinder shares V = π r² h, but its lateral and total surface areas need 3D coordinates instead of the 2π r h and 2π r (h + r) forms used here.
• • The page assumes a single solid cylinder with two parallel circular bases. For a hollow cylinder, a frustum, or a truncated cylinder, the geometry changes and separate formulas are needed.
• • Capacity in liters and US gallons uses fixed volume conversions of pure liquid. For real liquids (oils, fuels, brine) the mass in kilograms or pounds uses the actual liquid density.

The volume formula V = π r² h has a clean geometric check: it is exactly the area of the circular base times the height.

According to Wikipedia (Cylinder article), a right circular cylinder is a cylinder whose axis is perpendicular to the bases, with volume V = π r^2 h and total surface area A = 2 π r (r + h)

If the top of the cylinder narrows to a point, the geometry becomes a right circular cone, and the Cone Volume Calculator page returns the (1/3) · π · r² · h cone volume in the same metric and imperial units.