Tank Volume Calculator
Volume at any liquid level for tanks with real heads — plus mass, ullage and a dip chart.
Volume of each part (full)
| Part | Volume | Share |
|---|
Dip chart (strapping table)
| Level | Volume | Full |
|---|
Formulas used
About the Tank Volume Calculator
Work out how much liquid a tank or vessel holds at any level — and its full capacity — for vertical and horizontal cylinders with flat, hemispherical, 2:1 ellipsoidal, torispherical (ASME flanged and dished, 80:10, Klöpper, Korbbogen or your own radii) or conical heads, and for capsule, cone-bottom, spherical and rectangular tanks. You also get the percentage full, the empty space (ullage), the mass of the liquid, the volume of each part, the level that holds a given volume, and a to-scale drawing of the fill.
The dip chart (strapping table) lists the volume at equal steps of level, in your units, and downloads as CSV for a dipstick or a level transmitter. Lying-down dished and conical heads are integrated slice by slice; every other case uses the exact closed-form formula, so the results do not depend on a rough approximation of the heads.
How to use it
- Choose the shape, the size unit and the unit for volumes.
- Enter the inside diameter and the straight length (lying) or height (upright) of the cylindrical part, measured between the tangent lines where the heads start. Pick each head type; for dished heads choose the standard or enter the crown and knuckle radii.
- Enter the liquid level measured up from the lowest point inside, or leave it empty for the full capacity. To find the level that holds a certain volume, enter it under “Find the level”.
- Pick the liquid (or enter its density) for the mass. Read the volume, % full and ullage, check the drawing, and set the level step for the dip chart — then download it or copy the result.
Examples
3,398 L of 17,802 L (19.1 % full). 10,000 L would stand 1.095 m deep.
Each head is 0.508 m deep and holds 2,187 L; capacity 32,648 L; 19,802 L when the level is 3 m
Cone 3,534 L + cylinder 28,274 L = 31,809 L; 1,047 L when the level is 1 m (still in the cone)
54.45 m³ of 523.6 m³ — a fifth of the height holds about a tenth of the volume
Common uses
- Converting a dipstick reading into litres or gallons for a diesel, oil or chemical tank
- Making a strapping chart for a new vessel or a level transmitter
- Checking how much a pressure vessel holds, including its dished ends
- Finding the alarm level that leaves a given safe ullage
Formulas
- Lying cylinder: V = L [R² acos((R − h) ÷ R) − (R − h) √(2Rh − h²)]
- Hemispherical heads (the two ends of a lying tank make a sphere): V = π h² (3R − h) ÷ 3; upright, one head to depth z: V = π z² (3R − z) ÷ 3
- 2:1 ellipsoidal heads (depth D/4): lying, two heads = (D/4 ÷ R) × π h² (3R − h) ÷ 3; upright, V(z) = π R² (a z² − z³/3) ÷ a² with a = D/4; full head = π D³ ÷ 24
- Cone of height c: V(z) = π R² z³ ÷ (3c²)
- Torispherical: a spherical crown of radius R_c joined to a toroidal knuckle of radius r_k; depth H = R_c − √((R_c − r_k)² − (R − r_k)²)
- Sphere: V = π h² (3R − h) ÷ 3
Dished heads compared
For an inside diameter D: an ASME flanged and dished head (crown D, knuckle 0.06 D) is 0.169 D deep and holds 0.0810 D³; an 80:10 head 0.226 D and 0.1099 D³; a Klöpper head (DIN 28011, crown D, knuckle 0.1 D) 0.194 D and 0.0990 D³; a Korbbogen head (DIN 28013, crown 0.8 D, knuckle 0.154 D) 0.254 D and 0.1308 D³; a 2:1 ellipsoidal head 0.25 D and 0.1309 D³; a hemispherical head 0.5 D and 0.2618 D³. The standards define the radii on the outside diameter; here they are applied to the diameter you enter, so use the inside diameter for capacity.
Measuring the level and dipping
Measure the level from the lowest point inside the tank — the bottom of the shell for a horizontal tank, the apex of the bottom head for an upright one. A dipstick reading taken through a top nozzle starts from the inside top, so subtract it from the inside height. For custody transfer and tax, tanks are calibrated by measurement (API MPMS Chapter 2.2A for upright tanks), which also accounts for tilt, deformation and internal fittings.
Sources
- ASME Boiler and Pressure Vessel Code Section VIII Div. 1, UG-32 (formed heads: hemispherical, 2:1 ellipsoidal, torispherical)
- DIN 28011 (Klöpper) and DIN 28013 (Korbbogen) dished heads
- API MPMS Chapter 2.2A, calibration of upright cylindrical tanks
- Circular-segment and spherical-cap geometry, and the volume integrals of solids of revolution
- EN 590 (diesel) and EN 228 (petrol) density limits at 15 °C
Limitations
- The tank is assumed level and undistorted, with smooth inside walls; internal pipes, coils, baffles and sludge are not subtracted.
- Heads are ideal shapes. Real formed heads have tolerances and a short straight flange (skirt); include the straight flange in the shell length.
- Density presets are typical values: liquid density changes with temperature, so for stock accounting use a measured density and a temperature correction.
- This is a geometric calculation, not a legal calibration for trade or tax.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How do I calculate the volume of liquid in a horizontal tank?
For the cylindrical part, multiply the area of the liquid’s circular segment, R² acos((R − h)/R) − (R − h)√(2Rh − h²), by the length; then add the liquid in the two heads. In a 2 m tank, 0.5 m of liquid is a quarter of the height but only 19.6 % of the cylinder’s volume.
What is a torispherical (dished) head?
A head made of a shallow spherical crown joined to the shell by a tightly curved knuckle. The common ASME flanged and dished head has a crown radius equal to the diameter and a knuckle radius of 6 % of it; it is 0.169 D deep and holds 0.081 D³.
How much does a 2:1 ellipsoidal head hold?
π D³ ÷ 24 ≈ 0.1309 D³ — exactly half of a spheroid with the shell’s radius and a depth of D/4. For a 2 m diameter that is 1.047 m³ (1,047 L) per head.
What is a dip chart or strapping table?
A table of volume against level, so that a level reading can be turned into a volume. Choose the level step (for example every centimetre or every inch) and download the table as CSV.
Where do I measure the liquid level from?
From the lowest point inside the tank. If you dip from the top, subtract your reading from the inside height to get the liquid level. Use inside dimensions throughout.
How is this different from the water tank capacity calculator?
The water tank capacity calculator is for household and building water storage and sizing by the number of people. This one covers industrial and process vessels: dished, ellipsoidal and conical heads in either orientation, spheres, the level for a target volume, liquid mass and a downloadable strapping table.