How to find the height of a cylinder
Here is how to find the height of a cylinder from its volume: divide the volume by the area of the base: h = V ÷ (πr²). Square the radius, multiply by π, then divide the volume by that number. From the surface area, use h = A ÷ (2πr) − r, or h = L ÷ (2πr) for the curved side alone.
Contents
h = V ÷ (π × r²). With V = 226.19 in³ and r = 3 in: h = 226.19 ÷ 28.274 = 8.00 in.
The height of a cylinder calculator above works from the volume, the total surface area or the lateral area, with the radius or the diameter. The sections below explain each formula, then apply them to tanks sized in gallons and liters.
Height of a cylinder formula
The height (or length) of a cylinder is the distance between its two circular ends, measured square to them. Each formula below is a standard cylinder formula rearranged for h.
| You know | Height formula | Example | Height |
|---|---|---|---|
| Volume V and radius r | h = V ÷ (πr²) | V = 900 cm³, r = 5 cm | 11.46 cm |
| Volume V and diameter d | h = 4V ÷ (πd²) | V = 1,000 cm³, d = 10 cm | 12.73 cm |
| Lateral area L and radius r | h = L ÷ (2πr) | L = 1,005.5 cm², r = 8 cm | 20.0 cm |
| Total area A and radius r | h = A ÷ (2πr) − r | A = 207.35 in², r = 3 in | 8.00 in |
How to find the height of a cylinder from the volume
The volume formula is V = πr²h, as shown in the guide on how to find the volume of a cylinder. The volume is the base area πr² times the height, so the height is the volume divided by the base area.
- Get the radiusIf you have the diameter, halve it. A 10 cm wide base has r = 5 cm.
- Match the unitsThe volume must be in the cube of the radius unit: cm³ with cm, in³ with inches. Convert liters (× 1,000 to cm³) or US gallons (× 231 to in³) first.
- Find the base areaπ × 5² = 25π ≈ 78.540 cm².
- Divide900 ÷ 78.540 ≈ 11.46 cm.
Check by going forward: π × 5² × 11.459 ≈ 900 cm³. If the check does not return your starting volume, a unit or a square is usually missing.
With the diameter instead of the radius
Since r² = d² ÷ 4, the formula becomes h = 4V ÷ (πd²). For one liter (1,000 cm³) in a 10 cm wide jar: 4 × 1,000 ÷ (π × 100) ≈ 12.73 cm. More on working with the width is on the page about the volume of a cylinder with the diameter.
Worked examples: tanks and containers
How tall for 50 US gallons, 20 in across?
Convert to cubic inches: 50 × 231 = 11,550 in³. The radius is 10 in, and the base area is π × 100 ≈ 314.16 in². The height is 11,550 ÷ 314.16 ≈ 36.76 in, a little over 3 ft of inside height.
How tall for 1,000 liters, 1.2 m across?
1,000 L = 1 m³. The radius is 0.6 m, the base area is π × 0.36 ≈ 1.1310 m², and the height is 1 ÷ 1.1310 ≈ 0.884 m, about 88 cm.
How tall for 300 US gallons, 4 ft across?
In cubic feet: 300 ÷ 7.48052 ≈ 40.104 ft³. The radius is 2 ft and the base area is π × 4 ≈ 12.566 ft². The height is 40.104 ÷ 12.566 ≈ 3.19 ft, about 38.3 in. The cylindrical tank volume calculator goes the other way and gives the gallons at any fill depth.
How deep is 2 ft³ in a form 1 ft across?
A round form 12 in wide has r = 0.5 ft and a base area of π × 0.25 ≈ 0.7854 ft². Two cubic feet fill it to 2 ÷ 0.7854 ≈ 2.55 ft, about 30.6 in.
Water level for one liter in a jar of radius 4 cm
Base area π × 16 ≈ 50.265 cm². One liter is 1,000 cm³, so the water stands 1,000 ÷ 50.265 ≈ 19.89 cm deep. This is also how a graduated cylinder works: each centimeter of height in that jar holds about 50.27 mL.
How to find the height of a cylinder from its surface area
From the lateral area
The curved side of a cylinder unrolls into a rectangle. Its width is the circumference 2πr and its height is h, so L = 2πrh and h = L ÷ (2πr). For a radius of 8 cm and a lateral surface area of 1,005.5 cm²: 2π × 8 ≈ 50.265, and h = 1,005.5 ÷ 50.265 ≈ 20.0 cm. The page on the lateral surface area of a cylinder covers labels, wraps and sleeves.
From the total surface area
The total area is A = 2πr² + 2πrh. Subtract the two ends, then divide by the circumference: h = (A − 2πr²) ÷ (2πr), which simplifies to h = A ÷ (2πr) − r. For A = 207.35 in² and r = 3 in: 2π × 3 ≈ 18.850, 207.35 ÷ 18.850 ≈ 11.000, minus 3 gives 8.00 in.
If the result is zero or negative, no cylinder of that radius has that area: the two ends alone already use it all. The calculator warns you in that case.
Height of a slanted cylinder
For a leaning cylinder, the height in V = πr²h is the perpendicular height, measured straight up from the base, not the length of the slanted side. The two are linked by the angle of the lean: perpendicular height = slant length × sin(angle with the base). The page on the oblique cylinder volume works through it.
Common mistakes when finding the height
Dividing the volume by πr instead of πr² is the most common slip. With V = 900 cm³ and r = 5 cm, 900 ÷ (π × 5) gives 57.3, five times the real height of 11.46 cm.
- Using the diameter as the radius. The base area comes out four times too big, so the height comes out four times too small.
- Gallons or liters left as they are. A volume in gallons divided by an area in square inches gives no meaningful length. Convert to in³ or cm³ first.
- Forgetting the ends in the total area. h = A ÷ (2πr) alone ignores the two circles; subtract r afterwards.
- Inside versus outside size. For capacity, the inside radius sets the height a liquid reaches.
To solve for the other dimension, the guide on how to find the radius of a cylinder rearranges the same formula for r. When you have both dimensions, the cylinder volume calculator checks the result in one step.
FAQ
What is the height of a cylinder formula?
From the volume: h = V ÷ (πr²). From the lateral area: h = L ÷ (2πr). From the total surface area: h = A ÷ (2πr) − r. In each case r is the radius of the base.
How do I calculate the height of a cylinder from volume and radius?
Square the radius, multiply by π, and divide the volume by the result. A volume of 900 cm³ with a radius of 5 cm gives h = 900 ÷ (π × 25) ≈ 11.46 cm.
How do I find the height of a cylinder from its surface area?
Divide the total area by 2πr, then subtract r: h = A ÷ (2πr) − r. For A = 207.35 in² and r = 3 in, h = 207.35 ÷ 18.85 − 3 ≈ 8.00 in.
What is the height of a cylinder with a radius of 8 cm and a lateral surface area of 1005.5 cm²?
h = L ÷ (2πr) = 1,005.5 ÷ (2 × π × 8) = 1,005.5 ÷ 50.265 ≈ 20.0 cm.
Is the height of a cylinder the same as its length?
Yes. Height and length both mean the distance between the two circular ends. A standing tank has a height; a pipe or a tank lying down has a length. The formulas are the same.
Related
- Radius of a cylinderHow to find the radius of a cylinder from its volume, surface area, circumference or diameter. Formulas, calculator and worked examples in inches and cm.
- How to find the volumeHow to find the volume of a cylinder: square the radius, multiply by π and the height. Worked examples in inches, feet, cm and m, plus common mistakes.
- Cylinder tank volumeTank volume calculator for vertical and horizontal cylinder tanks, full or partly filled. Get the capacity in gallons and liters, with worked examples.
Updated October 12, 2026