📌 This guide covers the exact tank volume formula for every major tank shape — cylinder, rectangular, horizontal, elliptical, and dish end with step-by-step worked examples and instant unit conversions.
Whether you are an engineer sizing a pressure vessel, a farmer planning irrigation storage, or a homeowner checking your water tank capacity, you need the right tank volume formula — and you need to know how to apply it correctly.
Different tank shapes require completely different mathematical formulas. Using the wrong formula, or making a small error in plugging in values, can lead to costly undersizing or dangerous overflow situations.
In this guide, we cover the tank volume formulas for every common shape – vertical cylinder, rectangular, horizontal cylinder, elliptical, and dish end tanks with clear diagrams, variable definitions, and fully worked step-by-step calculation examples.
Before applying any tank volume formula, you need to understand the geometry of the tank you are working with. Tank geometry determines which formula applies and which dimensions you need to measure.
Every tank volume formula is derived from basic geometric principles. The volume of any three-dimensional shape is calculated by understanding its cross-sectional area and how that area extends across its length, height, or depth.
Key Dimensions You Need to Measure
Diameter (D) — the full width across the circular cross-section of a cylinder
Radius (r) — half the diameter; always use this in formulas, never the full diameter
Height (h) — the vertical distance from base to top of a vertical tank
Length (L) — the horizontal axis of a horizontal or elliptical tank
Semi-major axis (a) — half the larger diameter of an ellipse
Semi-minor axis (b) — half the smaller diameter of an ellipse
Tank Shape
Key Dimensions
Formula Type
Typical Use
Vertical Cylinder
r, h
π × r² × h
Water towers
Rectangular
L, W, H
L × W × H
Pools, sumps
Horizontal Cylinder
r, L
π × r² × L
Fuel tankers
Elliptical
a, b, L
π × a × b × L
Pressure vessels
Dish End
r, L, dish depth
Cylinder + end caps
Chemical reactors
Capsule
r, h
Cylinder + sphere
Gas cylinders
A Critical Rule: Always Use Radius, Not Diameter
⚠️ Important: Every circular tank formula uses radius (r = D ÷ 2). If you measure the diameter as 3 meters, your radius is 1.5 meters. Entering the diameter directly in the formula will give you a result that is 4 times too large — a very common and costly mistake.
Unit Consistency
Always use the same unit for every dimension in your calculation. If you measure in meters, your result will be in cubic meters (m³). Multiply by 1,000 to convert to litres. If you measure in feet, your result is in cubic feet (ft³) — multiply by 28.317 for litres.
Cylinder Volume Formula (Vertical Tank)
The vertical cylindrical tank is the most widely used tank shape globally. This includes overhead water tanks, industrial storage vessels, grain silos, and well casings. Its circular cross-section and uniform height make it one of the simplest shapes to calculate.
📐 Vertical Cylindrical Tank
V = π × r² × hWhere: V = volume of the tank (cubic meters, cubic feet, etc.) π = pi = 3.14159 r = radius of the circular base (= Diameter ÷ 2) h = height (or depth) of the tank
Worked Example — Vertical Cylinder
📋 Problem: A vertical cylindrical water tank has a diameter of 3 meters and a height of 4 meters. Calculate the total volume in cubic meters and litres.
Step 1
Identify the radius r = Diameter ÷ 2 = 3 ÷ 2 = 1.5 meters
Step 2
Write the formula V = π × r² × h
Step 3
Substitute the values V = 3.14159 × (1.5)² × 4 V = 3.14159 × 2.25 × 4
Step 4
Calculate V = 3.14159 × 9 = 28.274 m³
Step 5
Convert to litres V = 28.274 × 1,000 = 28,274 litres
✅ Answer: The cylindrical tank holds 28.274 m³ or approximately 28,274 litres.
Rectangular tanks also called box tanks or cuboid tanks have four flat sides, a flat base, and a flat top. They are extremely common in swimming pools, underground sumps, aquarium tanks, chemical storage, and agricultural water storage pits.
The rectangular tank volume formula is the simplest of all tank geometries, requiring only three linear measurements.
📐 Rectangular (Cuboid) Tank
V = L × W × HWhere: V = volume of the tank L = internal length of the tank W = internal width of the tank H = internal height (depth) of the tank Note: Always measure internal dimensions to get usable volume.
Worked Example — Rectangular Tank
📋 Problem: A rectangular concrete water storage tank measures 5 m long, 3 m wide, and 2.5 m deep (internal dimensions). Calculate its total capacity.
Step 1
Identify all three dimensions L = 5 m, W = 3 m, H = 2.5 m
Step 2
Apply the formula V = L × W × H
Step 3
Substitute and calculate V = 5 × 3 × 2.5 = 37.5 m³
Step 4
Convert to litres V = 37.5 × 1,000 = 37,500 litres
✅ Answer: The rectangular tank holds 37.5 m³ or 37,500 litres.
💡 Practical Tip: For a swimming pool, measure the average depth if the floor slopes. Use (shallow end depth + deep end depth) ÷ 2 as your effective H value.
Horizontal Cylinder Tank Volume Formula
Horizontal cylindrical tanks lie on their side, with the circular cross-section facing the viewer. Common examples include fuel tankers, road transport tanks, underground petrol station tanks, septic tanks, and propane storage vessels.
When a horizontal cylinder is completely full, the volume formula is the same as for a vertical cylinder — only the orientation changes. The length (L) of the tank takes the place of height (h).
📐 Horizontal Cylindrical Tank (Full)
V = π × r² × LWhere: V = total volume of the tank r = radius of the circular cross-section (= Diameter ÷ 2) L = total length of the horizontal tank (the long axis)
Worked Example — Horizontal Cylindrical Tank (Full)
📋 Problem: A horizontal fuel storage tank has a diameter of 2 m and a total length of 8 m. Calculate the full volume.
Step 1
Find the radius r = 2 ÷ 2 = 1 meter
Step 2
Apply the formula V = π × r² × L
Step 3
Substitute the values V = 3.14159 × (1)² × 8 = 3.14159 × 8
Step 4
Calculate V = 25.133 m³
Step 5
Convert to litres V = 25,133 litres
✅ Answer: The horizontal tank holds 25.133 m³ or 25,133 litres when completely full.
Partial Fill Volume — Horizontal Cylinder
Calculating the volume of liquid in a partially filled horizontal cylinder is significantly more complex. It requires a trigonometric formula based on the liquid depth (d) inside the tank.
📐 Partial Fill — Horizontal Cylinder
V = L × [r² × arccos((r−d)/r) − (r−d) × √(2rd − d²)]Where: d = current depth of liquid measured from the bottom of the tank r = radius of the cylinder L = length of the cylinder This formula accounts for the curved geometry of the tank bottom. For practical use, our online calculator handles this automatically.
💡 For partial fill calculations on horizontal cylinders, use our free Tank Volume Calculator to get instant, accurate results without solving the trigonometric formula manually.
Elliptical Tank Volume Formula
Elliptical tanks have an oval cross-section rather than a circular one. They are used in road tankers, railway wagons, and industrial pressure vessels because the elliptical shape provides greater structural strength and a lower center of gravity compared to circular tanks of the same width.
📐 Elliptical Tank
V = π × a × b × LWhere: V = volume of the tank a = semi-major axis = half of the larger (wider) diameter b = semi-minor axis = half of the smaller (narrower) diameter L = length of the tank along its long horizontal axis Note: If the cross-section were circular, a and b would be equal and equal to r — making this identical to the cylinder formula.
Worked Example — Elliptical Tank
📋 Problem: An elliptical road tanker is 6 m long. Its cross-section has a major axis (wider diameter) of 2.4 m and a minor axis (narrower diameter) of 1.6 m.
Step 1
Find the semi-major axis (a) a = 2.4 ÷ 2 = 1.2 meters
Step 2
Find the semi-minor axis (b) b = 1.6 ÷ 2 = 0.8 meters
Step 3
Apply the formula V = π × a × b × L
Step 4
Substitute the values V = 3.14159 × 1.2 × 0.8 × 6
Step 5
Calculate V = 3.14159 × 5.76 = 18.096 m³
Step 6
Convert to litres V = 18,096 litres
✅ Answer: The elliptical tank holds 18.096 m³ or approximately 18,096 litres.
Dish End Tank Volume Formula
Dish end tanks also known as torispherical head tanks or hemispherical head tanks — consist of a cylindrical shell with one or two curved end caps. They are the standard design for pressure vessels in chemical plants, refineries, pharmaceutical facilities, and food processing.
The curved dish ends are not flat — they extend beyond the cylindrical shell and add meaningful volume. Ignoring the dish end volumes is a common mistake that can underestimate total capacity by 10 to 20 percent.
Type 1: Hemispherical Dish End
📐 Hemispherical Dish End Tank (Two Ends)
V = (π × r² × L) + (4/3 × π × r³)Where: V_cylinder = π × r² × L (the cylindrical body) V_sphere = (4/3) × π × r³ (both hemispherical ends together = one full sphere) r = radius of the cylindrical shell L = length of the cylindrical body only (excluding the end caps)
Type 2: Torispherical (Standard Dish End)
📐 Torispherical Dish End — Approximate Formula
V_each_end ≈ 0.0847 × D³Where: D = outer diameter of the cylindrical shell 0.0847 is the standard coefficient for a torispherical head with: Crown radius = D (full diameter) Knuckle radius = 0.1 × D For two torispherical ends: V_ends = 2 × 0.0847 × D³ = 0.1694 × D³ Total volume = V_cylinder + V_ends
Worked Example — Hemispherical Dish End Tank
📋 Problem: A pressure vessel has a cylindrical shell of radius 0.6 m and body length 4 m. Both ends are hemispherical. Calculate total volume.
Convert to litres V = 5.429 × 1,000 = 5,429 litres
✅ Answer: The dish end pressure vessel holds 5.429 m³ or 5,429 litres total.
💡 Notice: The dish ends contribute 0.905 m³ out of 5.429 m³ total — that is 16.7% of total capacity. This shows why ignoring dish ends causes significant under-calculation.
Tank Volume Formula Summary — All Shapes at a Glance
The table below provides a quick-reference summary of every tank volume formula covered in this guide. Bookmark this page or save the table for easy reference during your calculations.
Tank Shape
Volume Formula
Key Variables
Output
Vertical Cylinder
V = π × r² × h
r, h
m³ → ×1000 = L
Rectangular
V = L × W × H
L, W, H
m³ → ×1000 = L
Horizontal Cylinder (Full)
V = π × r² × L
r, L
m³ → ×1000 = L
Elliptical
V = π × a × b × L
a, b, L
m³ → ×1000 = L
Dish End (Hemispherical)
V = π r²L + 4/3 π r³
r, L
m³ → ×1000 = L
Capsule
V = π r²h + 4/3 π r³
r, h (cyl only)
m³ → ×1000 = L
Unit Conversion Reference for Tank Volume
After calculating tank volume in cubic meters or cubic feet, you often need to convert to litres or gallons for practical use. Use the table below as a quick reference:
From Unit
To Unit
Multiply By
Cubic Meters (m³)
Litres (L)
1,000
Cubic Feet (ft³)
Litres (L)
28.317
Cubic Feet (ft³)
US Gallons
7.481
Litres (L)
US Gallons
0.2642
Litres (L)
Imperial Gallons
0.2200
US Gallons
Litres (L)
3.7854
Use Our Free Tank Volume Calculator
While understanding the formulas is valuable, real-world projects often involve multiple calculations, different units, and the need for instant accuracy. Our free online tank volume calculator eliminates manual calculation errors and gives you results in seconds.
🔗 Free Tank Volume Calculator — Supports all tank shapes. Outputs in litres, gallons, and cubic meters. Use it at: tankvolume-calculator.com
The calculator is particularly useful for:
Partial fill calculations on horizontal tanks (avoids the complex arccos formula)
Instant unit conversions between litres, gallons, and cubic meters
Comparing capacity across multiple tank shapes and sizes
Field use on mobile devices without carrying formula sheets
Common Mistakes When Applying Tank Volume Formulas
Using Diameter Instead of Radius
The most frequent mistake across all circular tank formulas. The formula requires r (radius). If you measure a diameter of 4 m, your r = 2 m. Inserting 4 m directly into the formula produces a volume that is exactly 4 times too large.
Inconsistent Units
Mixing meters and centimeters — or feet and inches — in the same calculation is the second most common error. For example, if you enter length in meters but depth in centimeters without converting, your answer will be 100 times off. Always standardize units before calculating.
Ignoring Internal vs External Dimensions
Thick-walled tanks, especially reinforced concrete cisterns, can have wall thicknesses of 15–30 cm or more. Using external dimensions instead of internal dimensions can overstate usable capacity by several thousand litres in large tanks.
Forgetting Dish End or Cap Volumes
For dish end tanks, capsule tanks, and domed tanks, calculating only the cylindrical body volume can understate actual capacity by 10–20%. Always add the end cap volume separately.
Technical Reference
For further reading on geometric volume formulas and their engineering applications, the following authoritative source provides comprehensive reference data:
A: The formula depends on the tank shape. For a cylindrical tank, use V = π × r² × h (vertical) or V = π × r² × L (horizontal). For a rectangular tank, use V = L × W × H. For an elliptical tank, use V = π × a × b × L. Dish end tanks require adding the end cap volume to the cylindrical body volume.
Q: How do I calculate the volume of a cylindrical tank in litres?
A: First, calculate the volume in cubic meters using V = π × r² × h. Then multiply by 1,000 to convert to litres. For example, a tank with radius 1 m and height 3 m has V = 3.14159 × 1 × 3 = 9.42 m³ = 9,420 litres.
Q: What is the difference between a vertical and horizontal cylinder tank formula?
A: Both use the same base formula: V = π × r². For a vertical tank, you multiply by height (h). For a horizontal tank, you multiply by length (L). When the horizontal tank is partially filled, a more complex trigonometric formula involving arccos is required.
Q: How do I calculate an elliptical tank volume?
A: Use the formula V = π × a × b × L, where a is the semi-major axis (half the larger diameter), b is the semi-minor axis (half the smaller diameter), and L is the length of the tank. This is similar to the cylinder formula but uses two different radii for the oval cross-section.
Q: Why is my tank volume calculation wrong?
A: The most likely causes are: (1) using diameter instead of radius in the formula — you must divide diameter by 2 first; (2) mixing units such as meters and centimeters; (3) using the wrong formula for the tank shape; or (4) using external dimensions instead of internal for thick-walled tanks.
Q: How do I calculate partial fill volume for a horizontal cylinder?
A: Use the formula V = L × [r² × arccos((r−d)/r) − (r−d) × √(2rd − d²)], where d is the current liquid depth and r is the radius. This trigonometric formula can be complex to solve by hand, so using an online partial-fill tank calculator is strongly recommended.
Q: How many litres is 1 cubic meter?
A: Exactly 1,000 litres. This conversion is consistent and precise: 1 m³ = 1,000 litres, regardless of the shape or context of the calculation.
Q: What is a dish end tank and how is its volume calculated?
A: A dish end tank has a cylindrical body with curved (dished) end caps. To calculate its volume, add the cylindrical body volume (π × r² × L) to the volume contributed by the end caps. For hemispherical ends, both caps together equal one full sphere with volume (4/3) × π × r³. Standard torispherical ends use the approximate formula 0.0847 × D³ per end.
Conclusion
Every tank shape has its own specific volume formula — and using the correct formula with accurate measurements is the foundation of reliable tank capacity calculation. The key formulas to remember are: V = π × r² × h for vertical cylinders, V = L × W × H for rectangular tanks, V = π × r² × L for horizontal cylinders, V = π × a × b × L for elliptical tanks, and the two-component formula for dish end vessels.
Across all formulas, the most important rule is always to use radius (not diameter) and to keep all measurements in the same unit. For dish end tanks, always include the end cap contribution to avoid significantly underestimating capacity.
For fast, accurate, and error-free results in your next project, use our free online tank volume calculator — it handles every shape, supports all units, and includes partial fill calculation for horizontal cylinders.
🔗 Get instant results with our free Tank Volume Calculator — no manual formulas required. Visit: tankvolume-calculator.com
