Height of a Cylinder Calculator
Calculate cylinder height using volume, surface areas, radius, or diagonal
Calculate Cylinder Height
⚠️ Both radius and volume must be positive
Cylinder Height Formulas
Volume & Radius
h = V/(πr²)
Lateral Area & Radius
h = A_l/(2πr)
Total Area & Radius
h = (A-2πr²)/(2πr)
Diagonal & Radius
h = √(d²-4r²)
Volume & Base Area
h = V/(A_b/2)
Lateral & Total Area
h = A_l/(2π√((A-A_l)/(2π)))
Quick Examples
Example 1: Water Tank
Radius: 5 cm
Volume: 900 cm³
Height: 11.46 cm
Example 2: Pipe Section
Radius: 8 cm
Lateral Area: 1005.5 cm²
Height: 20 cm
Key Concepts
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Right Cylinder: Circular bases directly aligned
📐
Height: Perpendicular distance between bases
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Lateral Area: Curved surface area
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Total Area: Base area + lateral area
Understanding Cylinder Height Calculations
What is a Cylinder?
A right circular cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface. The height is the perpendicular distance between the two bases.
Basic Cylinder Formulas
- •Volume: V = πr²h
- •Lateral Area: A_l = 2πrh
- •Base Area: A_b = 2πr² (both bases)
- •Total Area: A = A_b + A_l
Real-World Applications
Water Storage
Calculate tank heights for specific volume requirements.
Construction
Determine pipe dimensions and column specifications.
Manufacturing
Design cylindrical containers and mechanical parts.
Calculation Methods Overview
| Method | Required Parameters | Best Used When |
|---|---|---|
| Volume & Radius | V, r | Most common scenario |
| Lateral Area & Radius | A_l, r | Surface coating calculations |
| Total Area & Radius | A, r | Material usage planning |
| Diagonal & Radius | d, r | Structural design |