78.5398
units²
314.1593
units²
471.2389
units²
785.3982
units³
78.5398
units²
314.1593
units²
471.2389
units²
785.3982
units³
The Cylinder Volume Calculator determines how much three-dimensional space a cylinder occupies, given its radius and height. A right circular cylinder is defined by a circular base of radius $$r$$ and a perpendicular height $$h$$. This is the most commonly needed cylinder calculation—from sizing storage tanks to determining pipe capacity to computing the volume of a drinking glass.
$$V = \pi r^2 h$$
This elegant formula multiplies the area of the circular base ($$\pi r^2$$) by the height ($$h$$). It can be derived several ways:
Intuitive approach: A cylinder is a stack of infinitely thin circular discs, each of area $$\pi r^2$$. Stacking them to height $$h$$ gives total volume $$\pi r^2 h$$.
Integral calculus:
$$V = \int_0^h \pi r^2 \, dz = \pi r^2 h$$
Since the cross-section is constant, the integral simply multiplies the cross-sectional area by the height.
Cavalieri’s Principle: Two solids with equal cross-sectional areas at every height have equal volumes. A cylinder and a rectangular prism with the same cross-sectional area and height have the same volume.
If you know the diameter $$d$$ rather than the radius, substitute $$r = d/2$$:
$$V = \pi \left(\frac{d}{2}\right)^2 h = \frac{\pi d^2 h}{4}$$
Cylinder volume in cm³ converts directly to milliliters (1 cm³ = 1 mL). Useful conversions:
Water tanks: A cylindrical water tank with radius 2 m and height 5 m holds $$\pi(2)^2(5) = 20\pi \approx 62.83$$ m³ = 62,832 liters.
Engine displacement: Each cylinder in a car engine is modeled as a cylinder. Bore (diameter) and stroke (height) determine the displacement volume. A 4-cylinder engine with bore 86 mm and stroke 86 mm has total displacement of $$4 \times \pi(43)^2(86) \approx 1,998,000$$ mm³ ≈ 2.0 liters.
Cooking: Round cake pans are cylinders. An 8-inch (20.3 cm) round pan that is 2 inches (5.1 cm) deep holds about $$\pi(10.15)^2(5.1) \approx 1651$$ cm³ of batter.
Civil engineering: Concrete columns, piles, and drill holes are all cylindrical. Accurate volume estimates prevent material waste and cost overruns.
Enter the radius and height for an instant result.
Input the radius $$r$$ and height $$h$$ of the cylinder. The calculator computes $$V = \pi r^2 h$$ and returns the volume in cubic units. If you know the diameter, divide it by 2 before entering.
The result is the volume in cubic units matching your inputs. To convert to liters (if inputs are in cm), divide by 1000. For a partially filled horizontal cylinder, the volume depends on the fill height and requires a more complex formula involving an inverse cosine function.
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A circular pool of radius 4 m and depth 1.5 m holds V = π(4)²(1.5) ≈ 75.4 m³ = 75,398 liters of water.
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Results
A glass with radius 3.5 cm and height 12 cm holds ≈461.8 cm³ ≈ 462 mL, which is roughly a standard pint (473 mL).
Divide the diameter by 2 to get the radius. For example, a 10 cm diameter cylinder has radius 5 cm. Enter 5 as the radius.
Yes, the volume formula $$V = \pi r^2 h$$ works for oblique cylinders as long as $$h$$ is the perpendicular height (the vertical distance between the two bases), not the slant length.
For a horizontal cylinder partially filled to depth $$d$$, the formula involves the inverse cosine: $$V = L \left[ r^2 \cos^{-1}\left(\frac{r-d}{r}\right) - (r-d)\sqrt{2rd - d^2} \right]$$, where $$L$$ is the cylinder length.
Engine displacement is the total swept volume of all cylinders in an engine: $$V = n \cdot \pi r^2 \cdot s$$, where $$n$$ is the number of cylinders, $$r$$ is the bore radius, and $$s$$ is the stroke length.
Volume is quadratically sensitive to radius ($$r^2$$) but only linearly to height. Doubling the radius quadruples the volume; doubling the height only doubles it. This is why wider containers hold much more than taller ones.
Yes, if you know the density: $$m = \rho V$$. For water, $$\rho = 1$$ g/cm³, so the volume in cm³ equals the mass in grams. For other materials, look up the specific density.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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