Cylinder Volume Calculator

Calculate cylinder volume from radius, diameter, or circumference. Convert results to liters, gallons, cc, m³, in³, ft³, or yd³. Also solve hollow, horizontal, frustum, and engine modes.

Calculate right circular cylinder capacity using the standard formula $V = \pi r^2 h$. Determine volume starting from base radius, diameter, or circumference. Results convert automatically into liters, US gallons, cubic centimeters (cc), cubic meters ($m^3$), cubic inches ($in^3$), cubic feet ($ft^3$), and cubic yards ($yd^3$). Dedicated modes also measure hollow cylinders, horizontal tanks, conical frustums, and engine displacement.

Supported Measurements

Calculation Method in Tool	Inputs Required	Main Output	Secondary Outputs	Best Use Case
Right Cylinder (from Radius)	Radius, height	Volume	Lateral area, total area	Direct geometry problems
Right Cylinder (from Diameter)	Diameter, height	Volume	Lateral area, total area	Standard tanks and pipes
Right Cylinder (from Circumference)	Circumference, height	Volume	Lateral area, total area	Wrapped exterior measurements
Hollow Cylinder	Outer diameter, inner diameter, height	Material volume	Inner capacity, total surface area	Pipe walls and tubing
Horizontal Cylinder	Tank diameter, tank length, liquid depth	Liquid volume	Total tank capacity, empty volume	Partially filled lying tanks
Conical Frustum	Bottom diameter, top diameter, height	Volume	Lateral area, total area	Tapered containers
Engine Cylinder Displacement	Bore, stroke, cylinder count	Total engine volume	Single-cylinder volume	Motor displacement calculations

Outputs by Calculator Mode

Calculator Mode	Primary Output	Additional Outputs
Standard Cylinder Modes	Total volume	Lateral area, total area
Hollow Cylinder	Material volume	Inner capacity, total surface area
Horizontal Cylinder	Liquid volume	Total tank capacity, empty volume
Conical Frustum	Total volume	Lateral area, total area
Engine Displacement	Total engine volume	Single cylinder volume

Cylinder Volume Formulas

Shape / Method	Formula	Variables
Right cylinder	$V = \pi r^2 h$	$r$ = radius, $h$ = height
Right cylinder from diameter	$V = \pi(d/2)^2 h$	$d$ = diameter
Right cylinder from circumference	$V = \pi(c / 2\pi)^2 h$	$c$ = circumference
Hollow cylinder wall volume	$V = \pi(R^2 – r^2)h$	$R$ = outer radius, $r$ = inner radius
Hollow cylinder inner capacity	$V = \pi r^2 h$	$r$ = inner radius
Horizontal cylinder liquid volume	$V = L \times [r^2 \arccos((r-h)/r) – (r-h)\sqrt{2rh-h^2}]$	$L$ = tank length, $r$ = radius, $h$ = liquid depth
Conical frustum	$V = (\pi h/12)(D^2 + Dd + d^2)$	$D$ = bottom diameter, $d$ = top diameter
Engine displacement per cylinder	$V = \pi(B/2)^2 S$	$B$ = bore, $S$ = stroke
Total engine displacement	$V = \pi(B/2)^2 S \times N$	$N$ = number of cylinders

How to Calculate Cylinder Volume with This Tool

If you know…	Choose tool mode	Enter values
Radius and height	Right Cylinder (from Radius)	Radius, height
Diameter and height	Right Cylinder (from Diameter)	Diameter, height
Circumference and height	Right Cylinder (from Circumference)	Circumference, height
Outer and inner diameter	Hollow Cylinder	Outer diameter, inner diameter, height
Tank dip depth	Horizontal Cylinder	Tank diameter, length, filled depth
Bore, stroke, cylinder count	Engine Cylinder Displacement	Bore, stroke, cylinders

Select a preferred unit from the output dropdown menu. The calculator takes the base metric calculation and instantly displays results in liters, gallons, cc, $m^3$, $in^3$, $ft^3$, or $yd^3$ without changing original inputs.

Supported Volume Units

Output Unit Available	Best For
Liters (L)	water, tanks, general metric capacity
Gallons (US)	fuel, water, tank capacity
cc	engine displacement, small volumes
$m^3$	engineering, construction, bulk storage
$in^3$	machining, engine, imperial geometry
$ft^3$	storage, tank capacity, construction
$yd^3$	large bulk volume measurement

Radius, Diameter, and Circumference Calculations

Known Measurement	Conversion Used Before Volume	Final Formula
Radius	None	$V = \pi r^2 h$
Diameter	$r = d/2$	$V = \pi(d/2)^2 h$
Circumference	$r = c / 2\pi$	$V = \pi(c / 2\pi)^2 h$

Radius inputs work best for direct geometry problems where half the circle distance is provided. Diameter inputs suit real-world objects like tanks, pipes, and structural columns requiring edge-to-edge measurements.

Circumference inputs help when taking wrap measurements around an existing pipe or post with a flexible tape measure.

Hollow Cylinder Volume and Inner Capacity

Hollow Cylinder Output	Meaning
Material Volume (Wall)	Solid material in pipe/tube wall
Inner Capacity (Volume)	Empty internal volume a hollow cylinder holds
Total Surface Area	Combined exposed area based on outer radius, inner radius, and height

Hollow Cylinder Formula	Use
$V = \pi(R^2 – r^2)h$	Wall/material volume
$V = \pi r^2 h$	Inner capacity

Horizontal Cylinder Tank Volume

Input	Meaning
Tank diameter	Full cylinder diameter
Tank length	End-to-end cylindrical length
Filled liquid depth	Measured liquid depth from bottom

Output	Meaning
Liquid Volume	Current liquid volume at entered fill depth
Total Tank Capacity	Full internal capacity when completely filled
Empty Volume	Remaining unfilled volume

Total capacity relies on standard cylinder geometry. Calculating partial fill uses a circular-segment formula. Such measurements help find current propane or water tank capacity from simple dipstick depth readings.

Conical Frustum Volume

Search Wording People Use	Calculated Geometry
tapered cylinder	conical frustum
conical cylinder	conical frustum

Formula	Meaning
$V = (\pi h/12)(D^2 + Dd + d^2)$	Volume of a conical frustum

Calculations handle tapered shapes featuring different top and bottom diameters. Tapered containers are not mathematically true right cylinders. Correct frustum geometry ensures accurate volume.

Engine Cylinder Displacement

Engine Input	Meaning
Bore	Cylinder diameter
Stroke	Distance piston travels
Number of cylinders	Total engine cylinders

Engine Output	Meaning
Total Engine Volume	Full engine displacement
Single Cylinder Volume	Swept volume of one cylinder

$\text{Displacement} = \pi(B/2)^2 \times \text{Stroke} \times \text{Number of Cylinders}$

Engine displacement usually relies on cubic centimeters (cc) or liters to express total size. Engine mode commonly uses millimeters for bore and stroke inputs, outputting the final displacement in cc or liters to match standard motor specifications.

Surface Area Results

Surface Area Result	Available Modes
Lateral Surface Area	Right cylinder, conical frustum
Total Surface Area	Right cylinder, hollow cylinder, conical frustum

Shape	Lateral Surface Area	Total Surface Area
Right cylinder	$A_L = 2\pi rh$	$A = 2\pi r(h + r)$
Conical frustum	$A_L = \pi(R + r)s$	$A = \pi(R + r)s + \pi R^2 + \pi r^2$

Validation Rules

Mode	Validation Rule
Standard cylinder modes	Entered dimensions must exceed zero
Hollow cylinder	Inner diameter must remain smaller than outer diameter
Horizontal cylinder	Diameter and length must exceed zero; filled depth cannot be negative or exceed diameter
Conical frustum	Bottom diameter and height must exceed zero; top diameter can be zero or more
Engine displacement	Bore and stroke must exceed zero; cylinder count requires an integer of at least 1

Worked Examples

Calculation Goal	Example Inputs	Output Focus
Find basic volume in liters	Radius 5 cm, height 10 cm	liters
Measure large tanks in gallons	Diameter 24 in, height 36 in	US gallons
Calculate space in cubic feet	Radius 1.5 ft, height 8 ft	$ft^3$
Find volume using diameter	Diameter 12 cm, height 25 cm	volume
Convert wrap measurement	Circumference 31.416 cm, height 10 cm	converted volume
Measure pipe wall material	Outer diameter 10 cm, inner diameter 8 cm, height 20 cm	wall volume and inner capacity
Check lying tank level	Diameter 10 ft, length 20 ft, liquid depth 4 ft	liquid volume and empty volume
Calculate motor size	Bore 84 mm, stroke 90 mm, 4 cylinders	cc / liters

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