Area & Volume Calculator

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cylinder volume calculator

Cylinder Volume Calculator

A right cylinder's volume is V = π × r² × h; its total surface area, adding the two circular caps to the lateral surface, is A = 2π × r × (r + h). For r = 4 cm and h = 10 cm, V = 160π ≈ 502.65 cm³.

Why V = πr²h

A right cylinder can be seen as a stack of identical circles of area π × r², piled up to height h; summing those slices gives V = π × r² × h, the same logic used for any prism (base area × height). Because the radius is squared in the formula, doubling r multiplies the volume by 4, while doubling h only doubles it: for r=4 cm and h=10 cm, V ≈ 502.65 cm³; doubling r to 8 cm raises the volume to ≈ 2010.62 cm³ (4×), but doubling h to 20 cm only raises it to ≈ 1005.31 cm³ (2×).
Total surface area adds three surfaces: the two circular caps, each with area π × r², plus the lateral surface, which unrolled becomes a rectangle of width 2π × r (the base circumference) and height h, area 2π × r × h. Adding it up: A = 2πr² + 2πrh = 2πr(r+h). For r=3 cm and h=12 cm: the two caps add up to 2×π×9 ≈ 56.55 cm², the lateral surface adds ≈ 226.19 cm², and the total is 282.74 cm², the same value 2πr(r+h) = 90π gives directly.
By the International System's definition, 1 cm³ equals exactly 1 milliliter and 1000 cm³ equal 1 liter; if radius and height are measured in centimeters, dividing the computed volume by 1000 gives liters. In the r=4 cm, h=10 cm example, V ≈ 502.65 cm³ corresponds to about 0.503 liter. That conversion does not apply to the surface area, which stays in cm² (an area unit, not a volume unit) and has no direct liter equivalent.

Examples

r = 4 cm, h = 10 cm

Input: r=4, h=10
Expected output: V ≈ 502.65 cm³, área total ≈ 351.86 cm²

V = π×16×10 = 160π; total area adds the two caps (2π×16≈100.53 cm²) to the lateral surface (2π×4×10≈251.33 cm²).

r = 3 cm, h = 12 cm

Input: r=3, h=12
Expected output: V ≈ 339.29 cm³, área total ≈ 282.74 cm²

Volume is 108π; converted to liters, 339.29 cm³ ≈ 0.339 L (divide by 1000).

r = 0.5 cm, h = 2 cm (small cylinder)

Input: r=0.5, h=2
Expected output: V ≈ 1.57 cm³, área total ≈ 7.85 cm²

The formula does not change for small dimensions: V=π×0.25×2=0.5π; the surface area (7.85 cm²) is larger than the volume only because cm² and cm³ are different units.

Full tool FAQ

What unit should I use?

Use any unit you prefer (cm, m, inches…). The area/volume will be in the corresponding squared/cubed unit. For example, if you enter cm, area will be in cm².

Why does the triangle perimeter show '—'?

Does the cone formula use the slant height?

What is the formula for circle area?

How do I calculate sphere volume?

What is a rectangular box?

Can I use this for physics problems?

How precise are the results?

Frequently asked questions

Does this result already come converted to liters?

No. The calculator returns the volume in the cubic unit matching your input, for example cm³ if radius and height were entered in centimeters. To convert to liters, divide by 1000, since 1000 cm³ equal exactly 1 liter; 502.65 cm³ becomes 0.50265 L.

Why is the total area larger than the lateral area alone?

Because total area adds the lateral surface (2πrh) to the two circular caps (2πr²). For r=4 cm and h=10 cm, the lateral surface is ≈ 251.33 cm² and the two caps together are ≈ 100.53 cm², totaling ≈ 351.86 cm².

What happens to the volume if I only double the radius?

It quadruples, because r is squared in V=πr²h. Doubling only the height h, by contrast, only doubles the volume, since h enters the formula linearly.

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cylinder volume calculator

Cylinder Volume Calculator

Why V = πr²h

A right cylinder can be seen as a stack of identical circles of area π × r², piled up to height h; summing those slices gives V = π × r² × h, the same logic used for any prism (base area × height). Because the radius is squared in the formula, doubling r multiplies the volume by 4, while doubling h only doubles it: for r=4 cm and h=10 cm, V ≈ 502.65 cm³; doubling r to 8 cm raises the volume to ≈ 2010.62 cm³ (4×), but doubling h to 20 cm only raises it to ≈ 1005.31 cm³ (2×).

Total surface area adds three surfaces: the two circular caps, each with area π × r², plus the lateral surface, which unrolled becomes a rectangle of width 2π × r (the base circumference) and height h, area 2π × r × h. Adding it up: A = 2πr² + 2πrh = 2πr(r+h). For r=3 cm and h=12 cm: the two caps add up to 2×π×9 ≈ 56.55 cm², the lateral surface adds ≈ 226.19 cm², and the total is 282.74 cm², the same value 2πr(r+h) = 90π gives directly.

By the International System's definition, 1 cm³ equals exactly 1 milliliter and 1000 cm³ equal 1 liter; if radius and height are measured in centimeters, dividing the computed volume by 1000 gives liters. In the r=4 cm, h=10 cm example, V ≈ 502.65 cm³ corresponds to about 0.503 liter. That conversion does not apply to the surface area, which stays in cm² (an area unit, not a volume unit) and has no direct liter equivalent.

Examples

r = 4 cm, h = 10 cm

Input: r=4, h=10
Expected output: V ≈ 502.65 cm³, área total ≈ 351.86 cm²

V = π×16×10 = 160π; total area adds the two caps (2π×16≈100.53 cm²) to the lateral surface (2π×4×10≈251.33 cm²).

r = 3 cm, h = 12 cm

Input: r=3, h=12
Expected output: V ≈ 339.29 cm³, área total ≈ 282.74 cm²

Volume is 108π; converted to liters, 339.29 cm³ ≈ 0.339 L (divide by 1000).

r = 0.5 cm, h = 2 cm (small cylinder)

Input: r=0.5, h=2
Expected output: V ≈ 1.57 cm³, área total ≈ 7.85 cm²

The formula does not change for small dimensions: V=π×0.25×2=0.5π; the surface area (7.85 cm²) is larger than the volume only because cm² and cm³ are different units.

Full tool FAQ

What unit should I use?

Use any unit you prefer (cm, m, inches…). The area/volume will be in the corresponding squared/cubed unit. For example, if you enter cm, area will be in cm².

Why does the triangle perimeter show '—'?

Does the cone formula use the slant height?

What is the formula for circle area?

How do I calculate sphere volume?

What is a rectangular box?

Can I use this for physics problems?

How precise are the results?

Frequently asked questions

Does this result already come converted to liters?

Why is the total area larger than the lateral area alone?

What happens to the volume if I only double the radius?

It quadruples, because r is squared in V=πr²h. Doubling only the height h, by contrast, only doubles the volume, since h enters the formula linearly.