Right Cylinder Calculator: find A, V, A_l, A_b

Calculate the right cylinder calculator: find a, v, a_l, a_b precisely — enter your dimensions and get the result with the formula shown.

Quick Facts

Volume
V = πr²h
Base area (πr²) times height.
Lateral (side) area
A_l = 2πrh
The curved side unrolled into a rectangle of width 2πr and height h.
Total surface area
A = 2πr² + 2πrh = 2πr(r + h)
Lateral area plus the two circular bases.

Your Results

Calculated
Volume (V)
-
V = πr²h
Total Surface Area (A)
-
A = 2πr² + 2πrh
Lateral Surface Area (A_l)
-
A_l = 2πrh
Base Area (A_b, one circle)
-
A_b = πr²

Ready

Enter a radius and height, then press Calculate.

Formula and Method for a Right Cylinder

A right circular cylinder is a solid with two parallel, congruent circular bases connected by a curved side that is perpendicular to those bases (unlike an oblique cylinder, where the sides lean). Every measurement follows from just two inputs: the radius r of the circular base and the height h between the bases. This calculator returns the volume, the total surface area, the lateral (side-only) surface area, and the area of a single base.

How the calculation works

The base is a circle, so its area is A_b = πr². The volume is that base area times the height: V = πr²h. The lateral surface area comes from imagining the curved side cut vertically and unrolled flat — it becomes a rectangle with width equal to the base's circumference (2πr) and height h, giving A_l = 2πrh. The total surface area adds both circular bases (top and bottom) to that lateral area: A = 2πr² + 2πrh, which factors to A = 2πr(r + h). Enter the radius and height in the same unit; the calculator reports volume in cubic units and area in square units of whatever you selected.

Common mistakes

  • Radius vs. diameter: if you measured across the circular base (the diameter), divide by 2 before entering it — using diameter as radius inflates the base area by 4× and the volume by 4×.
  • Forgetting the second base: lateral area (A_l = 2πrh) only covers the curved side. Total surface area needs both circles added: A = A_l + 2A_b, not A_l + A_b.
  • Mixed units: volume comes out in cubic units (ft³, m³) and area in square units (ft², m²) — a cylinder that is 3 ft radius by 10 ft tall has a volume near 283 ft³, not 283 ft.

Real-world applications

  • Tanks, silos, and pipes use volume to determine liquid, gas, or grain storage capacity.
  • Cans, pipes, and rollers use lateral area to calculate how much label, wrap, or coating material is needed.
  • Manufacturing and packaging use total surface area to estimate material and cost for a sealed cylindrical container.
  • Civil and mechanical engineering use these formulas for columns, drums, and cylindrical structural members.

Frequently Asked Questions

What is the formula for the volume of a right cylinder?
The volume of a right circular cylinder is V = πr²h, where r is the radius of the circular base and h is the height. A cylinder with a 3 ft radius and 10 ft height has a volume of π × 3² × 10 ≈ 282.74 ft³.
How do I find the total surface area of a cylinder?
Total surface area is A = 2πr² + 2πrh, or equivalently A = 2πr(r + h). This adds the area of the two circular bases (2πr²) to the lateral (side) area (2πrh).
What is the difference between lateral area and total surface area?
Lateral surface area, A_l = 2πrh, is just the curved side of the cylinder unrolled into a rectangle — it excludes the top and bottom circles. Total surface area adds both circular bases (2πr²) to the lateral area.
What if I only know the diameter instead of the radius?
Divide the diameter by 2 to get the radius (r = d/2) before using the volume or surface area formulas, since all right cylinder formulas are written in terms of radius, not diameter.

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