Cylinder Volume Calculator

Two boxes, pre-filled with r = 2 and h = 7. Click Calculate. The cylinder volume calculator form asks for exactly two numbers — the radius and the height of the cylinder.

• Radius r is the distance from the center of the circular base to its edge. Got a diameter instead? Halve it before typing it into the radius box of the cylinder volume calculator.
• Height h is measured straight up from the base, at right angles to it — not along a slanted side. Fill the optional outer-radius box R for a hollow pipe and the cylinder volume calculator adds the hollow row.
• Three answers come back at once: the cylinder volume calculator returns the volume V = πr²h, the total surface area, and the lateral (side-only) surface area. With the optional R filled, a fourth row hands over the hollow volume.

The cylinder volume calculator keeps π exact, so 2 and 7 return 28π ≈ 87.96 — the same answer your teacher wants to see.

This page is more than a static cylinder volume calculator — it is also an AI tutor you can ask questions:

• Ask in plain words. "What is the volume of a cylinder with radius 3 and height 10?" The AI fills the form and runs this cylinder volume calculator for you.
• Take a photo of your homework. The AI reads the numbers and fills the radius and height boxes for you.
• Ask about the ideas, not just the answer. "Why is the volume base times height?" The AI explains step by step — every number still comes from the cylinder volume calculator, so nothing is guessed.
• Keep asking follow-ups. Ask "why?" as often as you need — follow-up questions are welcome.
• Half-full tanks and tilted pipes. Odd shapes still start from this cylinder volume calculator; the AI shows how the same formula covers them.

A cylinder is a circle stacked straight up. That one sentence is the whole volume formula. The circle has area πr²; you stack it h times. The cylinder volume calculator multiplies the two: V = πr²h, "the base area times the height at right angles to the base." A bigger base or a taller stack makes the volume grow in direct proportion.

The picture behind the cylinder volume calculator shows the surface unrolled: the side of a cylinder is a rectangle 2πr wide (the circumference of the base) and h tall. That is why the side area is 2πrh — and why a soup-can label, which wraps exactly that rectangle, is a lateral-area question in disguise. Add the two circular ends, each πr², and the total surface area is 2πr² + 2πrh = 2πr(r + h). Both area answers ride along free in the cylinder volume calculator's second and third rows.

Read the picture first: circle for the base, rectangle for the side. Now the symbols the cylinder volume calculator uses:

$V = \pi r^2 h$

Every number the cylinder volume calculator returns comes from the three lines in this table.

One habit worth building: check units inside the cylinder volume calculator. Radius in centimeters and height in centimeters give volume in cubic centimeters; mix centimeters with meters and the answer is nonsense.

Run the classic pair through the cylinder volume calculator: r = 2 and h = 7.

1. Volume: $V = \pi r^2 h = \pi (2)^2 (7) = 28\pi \approx 87.96$.
2. Total surface area: $SA = 2\pi r(r+h) = 2\pi(2)(2+7) = 36\pi \approx 113.10$.
3. Lateral area: $L = 2\pi r h = 28\pi \approx 87.96$ — for this shape the side alone happens to equal the volume's number.

These exact values come pre-loaded in the cylinder volume calculator above — click Calculate and 28π and 36π confirm instantly.

A water tank puts the cylinder volume calculator to real use. The tank is a cylinder with radius 0.9 m, and the water inside stands 1.7 m deep. How much water is that?

1. The water itself is a cylinder: r = 0.9, h = 1.7.
2. $V = \pi (0.9)^2 (1.7) = 1.377\pi \approx 4.326$ cubic meters.
3. One cubic meter is 1,000 liters, so the tank holds about 4,326 liters.

Type 0.9 and 1.7 into the cylinder volume calculator above and it returns 4.33 — proof the formula, not luck, produced the answer. Checks like this take ten seconds and catch every slip.

Double the radius, keep the height, and let the cylinder volume calculator reveal the surprise: r = 5, h = 10 versus the smaller r = 2.5, h = 10.

1. Large: $V = \pi (5)^2(10) = 250\pi \approx 785.4$.
2. Small: $V = \pi (2.5)^2(10) = 62.5\pi \approx 196.3$.
3. Ratio: $785.4 / 196.3 = 4$ — doubling r multiplies the volume by four, because r enters the formula squared.

The cylinder volume calculator shows this instantly: change 2.5 to 5, click again, and the volume row of the cylinder volume calculator quadruples. Volume follows r², a fact worth feeling once.

Four slips the cylinder volume calculator catches every day:

1. Typing the diameter as the radius. Diameter 10 means r = 5. Entering 10 gives a cylinder volume calculator answer four times too big — the r² in $\pi r^2 h$ squares the error.
2. Measuring height along a slanted side. For a leaning cylinder the formula still holds, but h is the perpendicular height, "at right angles to the base" — never the slant length.
3. Reporting lateral area when the question wants total surface area. A label or paint-the-side question needs $2\pi rh$ only; the full surface adds both circular ends. Read which one the problem asks for before trusting the third row of the cylinder volume calculator.
4. Mixing units. r in inches with h in feet produces a number with no meaning. The cylinder volume calculator does not convert units; same units in both boxes, every time.