Choose whether to enter diameter or radius, pick your unit, and calculate
Input mode
Enter diameter (full width of sphere)
Diameter
⚠ Please enter a valid measurement greater than zero.
Your Results
Total Volume
—
Litres (L)
Cubic Metres
— m³
US Gallons
— gal
UK/Imperial Gallons
— gal
Cubic Feet
— ft³
Cubic Inches
— in³
Radius Used
— cm
Water Weight
— kg
Weight (lbs)
— lbs
Sphere Visual
📖 How To Use
How to Use This Spherical Tank Volume Calculator
Calculating the exact capacity of a spherical water tank takes just seconds:
Choose your input type
Select "Enter Diameter" if you know the full width of the sphere from one side to the other. Select "Enter Radius" if you know the distance from the centre to the edge — exactly half the diameter.
Enter your measurement
Type the diameter or radius value. Always measure the internal dimension for accurate water storage capacity. External measurements include wall thickness and will overstate the actual volume.
Select your unit
Choose ft, in, cm, m, or mm from the dropdown. The calculator converts everything internally to centimetres before applying the formula.
Hit Calculate
Results appear instantly — volume in litres, US gallons, UK gallons, cubic metres, cubic feet, and the water weight in kg and lbs. The note under the results shows the working in feet and gallons, and how much the sphere holds at a quarter, half and three-quarters of its depth. Copy or print with one click.
Tip: Spherical tanks are often specified by their nominal diameter on the product label. This may be the external diameter. Subtract twice the wall thickness (typically 5–15 mm, about ¼–½ in, for plastic; more for large steel spheres) to get the internal diameter before calculating.
📐 The Formula
Spherical Tank Volume Formula
The volume of a perfect sphere is calculated using the standard sphere volume formula from Euclidean geometry:
V = (4/3) × π × r³
Where r = radius (half the diameter)
If you know the diameter (d): V = (π/6) × d³
Litres (cm inputs): V (L) = ((4/3) × π × r³) ÷ 1,000
Cubic metres (m inputs): V (m³) = (4/3) × π × r³
US gallons (ft inputs): V (ft³) × 7.48
This calculator converts your input to centimetres first, applies the sphere formula, then converts the result to all standard volume units simultaneously. π is computed to full floating-point precision.
Step-by-Step Worked Example
Suppose you have a spherical tank with a 120 cm diameter (60 cm radius):
r = 60 cm
V = (4/3) × π × 60³
V = (4/3) × 3.14159 × 216,000
V = 904,779 cm³
V = 904.8 litres ≈ 239 US gallons
Partially Filled Spherical Tank
The water in a partly filled sphere forms a spherical cap. With a liquid depth h measured from the bottom:
Vcap = π × h² × (3r − h) ÷ 3
Fraction of full = f² × (3 − 2f), where f = h ÷ diameter
So a sphere filled to 10% of its depth holds only 2.8% of its volume; 25% depth holds 15.6%; 50% holds exactly half; 75% holds 84.4%; and 90% holds 97.2%. A level gauge on a spherical tank therefore needs a calibration chart, not a straight percentage.
Unit Conversion Reference
Unit
Equals Litres
From Litres
1 Litre (L)
1 L
× 1
1 Cubic Metre (m³)
1,000 L
÷ 1,000
1 US Gallon
3.785 L
÷ 3.785
1 UK Gallon
4.546 L
÷ 4.546
1 Cubic Foot (ft³)
28.317 L
÷ 28.317
1 Cubic Inch (in³)
0.01639 L
× 61.024
Water Weight
1 litre of fresh water weighs about 1 kg (2.2046 lb), and 1 US gallon about 8.34 lb. The exact figure is 0.998 kg per litre at 20 °C (68 °F), so 1 kg per litre is the standard rounding used for load estimates. In US units, 1 cubic foot = 7.48 US gallons and 1 US gallon = 231 cubic inches.
Below are typical spherical tank diameters and their calculated volumes. Use these as a quick reference when comparing options:
Diameter
Radius
Litres
US Gallons
UK Gallons
Full Weight
50 cm
25 cm
65.4
17.3
14.4
65 kg
80 cm
40 cm
268.1
70.8
59.0
268 kg
1.0 m
50 cm
523.6
138.3
115.2
524 kg
1.2 m
60 cm
904.8
239.0
199.0
905 kg
1.5 m
75 cm
1,767.1
466.8
388.7
1,767 kg
2.0 m
100 cm
4,188.8
1,106.6
921.4
4,189 kg
2.5 m
125 cm
8,181.2
2,161.3
1,799.6
8,181 kg
3.0 m
150 cm
14,137.2
3,734.6
3,109.7
14,137 kg
Note: All volumes calculated using V = (4/3) × π × r³ with r in cm, divided by 1,000 for litres. Always verify against your specific tank's internal dimensions.
🌐 Use Cases
When Do You Need a Spherical Water Tank?
Spherical tanks are a specialized but important tank geometry. Here's when this calculator is most useful:
🏭
Industrial & Chemical Storage
Spherical tanks distribute internal pressure uniformly — ideal for storing pressurized water, gases, and chemicals at elevated pressures.
🏗️
Elevated Water Towers
Many municipal water towers use a spherical or spheroid (flattened sphere) tank, which holds a lot of water for its surface area on a single supporting column.
🚢
Marine & Offshore
Spherical pressure vessels are used on LNG tankers and offshore platforms where structural strength and minimal weight matter.
🌱
Decorative & Garden
Ball-shaped garden water features and small spherical cisterns need precise volume calculations for pump sizing and water treatment dosing.
For household use, if you're sizing a spherical water feature or a compact rooftop sphere tank, this calculator gives the exact litres and gallons in one click, helping you pair it correctly with your pump size and chlorine dosage.
🧮 Worked Example
Worked example: a 6 ft spherical tank
A spherical tank measures 6 ft (1.83 m) across inside.
Volume: π ÷ 6 × 6³ = 113.10 ft³.
In gallons: 113.10 × 7.48 = 846 US gallons (3,203 L, 705 UK gallons).
Water weight when full: 846 × 8.34 ≈ 7,060 lb (3,200 kg).
At 18 in deep (a quarter of the diameter), it holds only 15.6% — about 132 gallons.
Because volume grows with the cube of the diameter, a sphere just 10% wider (6.6 ft) holds 33% more: about 1,126 gallons.
❓ FAQ
Frequently Asked Questions
How do I calculate the volume of a spherical water tank?
Use the formula V = (4/3) × π × r³, where r is the radius (half the diameter). With feet, multiply the cubic feet by 7.48 for US gallons; with centimetres, divide the result by 1,000 to get litres. This calculator does all of that automatically — just enter your diameter or radius and hit Calculate.
Should I enter diameter or radius for a sphere tank calculator?
Either works — just toggle the input mode to match what you have. Diameter is the full width from one side of the sphere to the other. Radius is exactly half of that. If your tank's spec sheet lists the nominal diameter (most do), use the Diameter mode.
What is the formula for spherical tank volume?
The standard formula is V = (4/3) × π × r³. If you know the diameter instead of the radius, the equivalent formula is V = (π/6) × d³. Both give the same result. This calculator uses full floating-point π for maximum accuracy.
How many litres does a 1-metre diameter sphere hold?
A perfect sphere with a 1-metre (100 cm, 39.4 in) diameter holds approximately 523.6 litres — or about 138 US gallons. The radius is 50 cm, and V = (4/3) × π × 50³ ÷ 1,000 = 523.6 L.
How heavy is a full spherical water tank?
Water weighs about 1 kg per litre, or 8.34 lb per US gallon. A spherical tank holding 1,000 litres (264 gallons) contains about 1,000 kg (2,200 lb) of water. Add the weight of the tank shell — a steel sphere can weigh hundreds of kilograms depending on its diameter and wall thickness — and its legs or stand. Always verify that your support structure can handle the combined load before filling.
Why are some water towers spherical?
A sphere is the shape that encloses the maximum volume for a given surface area. It also distributes internal pressure evenly across its surface — meaning no stress concentration at corners or edges. For elevated water storage, where hydrostatic pressure is significant, a sphere requires less material than a cylinder of equal volume, reducing both cost and weight on the support tower.
Can this calculator be used for partially filled spheres?
This calculator computes full-sphere volume, and the note under the results gives the volume at a quarter, half and three-quarters of the depth. For any other level use the spherical cap formula V = (π × h² ÷ 3) × (3r − h), where h is the depth of the water. Do not scale the full volume by the depth percentage — near the bottom that overstates the contents badly: 25% of the depth holds only 15.6% of the volume.
How does a spherical tank compare to a cylindrical tank of the same volume?
A sphere uses the least surface area of any shape for a given volume — about 13% less than the best-proportioned cylinder (one as tall as it is wide), and more compared with tall or squat cylinders. This means less material cost and less heat exchange with the environment. However, spherical tanks are harder to manufacture and install than cylindrical ones, making them more common in industrial and municipal settings than in residential use. Use our Cylindrical Tank Volume Calculator to compare.
✅ Sources & Review
Sources and review
The formulas are standard geometry; the conversion factors and figures on this page come from these references:
USGS Water Science School — Water Density: about 1 kg per litre (62.4 lb/ft³, 8.34 lb per US gallon).
Reviewed by John Mac, PE, Water Systems Specialist
Texas-licensed Professional Engineer with 13+ years in residential water storage and 180+ tank projects. John writes and reviews every calculator on this site.
