Cylinder Calculator
Calculate volume, surface area, lateral area, and other cylinder properties
Distance from center to edge of base
Distance between the two circular bases
Cylinder Properties
Volume
cubic units
Lateral Surface Area
square units
Total Surface Area
square units
Base Area
πr²
Diameter
2r
Base Circumference
2πr
Formulas Used
Volume
V = πr²h
Lateral Surface Area
LSA = 2πrh
Total Surface Area
TSA = 2πr(h + r)
Base Area
A = πr²
Diameter
d = 2r
Circumference
C = 2πr
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About Cylinder Calculator
What is a Cylinder?
A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface. It is one of the most common shapes in engineering, manufacturing, and everyday life—from cans and pipes to tanks and pillars.
How to Use This Calculator
- Enter Values: Input the radius (r) and height (h) of your cylinder
- Select Unit Type: Choose between different unit systems if needed
- View Results Instantly: All cylinder properties are calculated automatically
- Adjust Decimal Places: Customize precision using the decimal selector
Cylinder Formulas
Core Cylinder Formulas
| Property | Formula | Description |
|---|---|---|
| Volume | V = πr²h | Space inside the cylinder |
| Lateral Surface Area | LSA = 2πrh | Curved surface area (sides only) |
| Total Surface Area | TSA = 2πrh + 2πr² = 2πr(h + r) | All surfaces including bases |
| Base Area | A = πr² | Area of one circular base |
| Diameter | d = 2r | Width across the base |
| Base Circumference | C = 2πr | Perimeter of circular base |
Derived Formulas
From Volume (V) and Height (h):
- Radius: r = √(V / πh)
From Volume (V) and Radius (r):
- Height: h = V / πr²
From Lateral Surface Area (LSA):
- Radius or Height: Requires knowing one to find the other
Understanding Cylinder Properties
Volume (V)
The volume represents the total space enclosed within the cylinder. It's calculated by multiplying the base area (πr²) by the height (h).
Common uses:
- Calculating tank capacities
- Determining liquid storage volumes
- Computing material displacement
- Sizing containers and pipes
Lateral Surface Area (LSA)
The lateral surface area is the curved surface of the cylinder, excluding the top and bottom circular bases. If you "unrolled" the cylinder's side, it would form a rectangle with dimensions (2πr × h).
Common uses:
- Calculating material for cylindrical labels
- Determining paint needed for tanks
- Sizing wrapping material
Total Surface Area (TSA)
The total surface area includes both the lateral surface and the two circular bases. It represents all the outer surface of a closed cylinder.
Common uses:
- Calculating sheet metal requirements
- Determining coating or painting area
- Heat transfer calculations
Base Area
The area of one circular end of the cylinder. A cylinder has two identical bases, so the combined base area is 2πr².
Real-World Applications
Engineering & Manufacturing
- Designing pressure vessels and tanks
- Calculating pipe volumes and flow rates
- Sizing hydraulic and pneumatic cylinders
- Manufacturing cans and containers
Construction & Architecture
- Calculating concrete for cylindrical pillars
- Designing water tanks and silos
- Planning cylindrical structures
Everyday Life
- Determining beverage can volumes
- Calculating candle wax requirements
- Sizing flower vases and containers
FAQ
How do I find the radius from the volume?
Rearrange the volume formula V = πr²h to solve for r:
r = √(V / πh)
For example, if volume is 500 cubic units and height is 10 units, radius = √(500 / (π × 10)) ≈ 3.99 units.
What's the difference between lateral and total surface area?
- Lateral Surface Area (LSA) includes only the curved side (like a can without lids)
- Total Surface Area (TSA) includes the curved side plus both circular bases (complete can)
TSA = LSA + 2 × Base Area
How do cylinders relate to circles?
A cylinder is essentially a circle extended through a third dimension. The base of a cylinder is a circle, and all circle formulas (area = πr², circumference = 2πr) apply to the cylinder's base.
How accurate is this calculator?
This calculator uses JavaScript's built-in Math library, providing approximately 15-17 significant digits of precision. You can select 2, 4, 6, or 8 decimal places for displayed results.
What units should I use?
Use any consistent unit system. If radius is in centimeters and height is in centimeters:
- Volume will be in cubic centimeters (cm³)
- Surface areas will be in square centimeters (cm²)
Just ensure all inputs use the same unit.
Historical Note
The study of cylindrical geometry dates back to ancient civilizations. The formula for the volume of a cylinder (base area × height) was known to ancient Egyptians and was formalized by Greek mathematicians including Archimedes, who also related it to the sphere and cone in his famous treatises.
Disclaimer: This calculator is designed for educational and practical purposes. For critical engineering or construction applications, always verify calculations with professional tools and consult experts.