SettingsSettings for this calculationUS
The shape of the vessel holding the liquid, and which way up it stands.
Orientation matters as much as shape: a cylinder standing upright fills in step with depth, the same cylinder on its side does not. A capsule is a cylinder with hemispherical ends, chosen under the cylinder's ends. The two ovals are different: an elliptical tank is a smooth ellipse in section, a flat-sided oval has straight sides between half-round ends, and a straightedge laid against the side tells them apart.
Across the inside of the barrel, at its widest.
Measure the outside and take off twice the wall, or measure through the lid across the inside. A ribbed plastic tank is narrower inside than its ribs suggest; take the smooth inner wall.
Tools needed: Tape measure
The height of the straight barrel, not counting any dished or domed ends.
For a flat-bottomed tank this is the inside height to the top of the walls, or to the overflow if that is where the liquid stops. With dished or domed ends, measure seam to seam: the heads are added from the choice below.
Flat ends, shallow dished heads, or full half-spheres.
A flat end is a plain disc. The dished choice is the 2:1 ellipsoidal head, a quarter of the diameter deep, which is the one modelled; a shallower flanged-and-dished head holds less. A capsule has a half-sphere at each end. Both ends are taken as the same kind.
The dipstick reading, from the lowest point inside the tank up to the surface.
From the inside bottom, not from the ground or a plinth. To find the capacity alone, enter the full inside height or more; anything above the top is read as a full tank. A gauge that measures down from the top gives the empty space, not this — subtract it from the inside height first.
Tools needed: Dipstick or tape with a weight
How far above the inside bottom the lowest outlet or suction sits; zero if it drains from the very bottom.
Liquid below the outlet stays in the tank. Opens at zero because the right figure is the installation drawing's, not a rule of thumb: a floating suction, a side outlet above a sediment zone or a pump intake above the floor all leave a different amount behind.
Liquid in the tank
423 gal
Standing upright on a flat bottom, the tank has the same cross-section at every level, so depth and contents rise together and a dipstick marked in equal steps reads true from bottom to top.
- Capacity when full
- 1,374.79 gal
- Space left above the liquid
- 951.78 gal
- Liquid above the lowest draw-off
- 423.01 gal
- Depth as a share of the inside height
- 30.77 %
- Contents as a share of capacity
- 30.77 %
- Inside height, bottom to top
- 6.5 ft
- Contents in litres (L)
- 1,601.28 L
- Contents in cubic metres (m³)
- 1.6 m³
- Contents in US gallons (gal)
- 423.01 gal
- Contents in imperial gallons (imp gal)
- 352.23 imp gal
- Capacity in litres (L)
- 5,204.16 L
- Capacity in cubic metres (m³)
- 5.2 m³
- Capacity in US gallons (gal)
- 1,374.79 gal
- Capacity in imperial gallons (imp gal)
- 1,144.76 imp gal
They open the calculator with your figures already in it
Tank Volume Calculator (Litres and Gallons at Any Depth): 423 gal — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Neutrium, Volume and wetted area of partially filled horizontal vessels: the barrel as a circular segment, L(R² cos⁻¹((R − h)/R) − (R − h)√(2Rh − h²)); a hemispherical head πh²(3R − h)/6; a semi-ellipsoidal head D³C(π/12)(3(h/D)² − 2(h/D)³) with C = 1/2 for the ASME 2:1 head, whose depth is a quarter of the diameter, and C = 0.49951 + 0.10462 t/Do + 2.3227 (t/Do)² for a DIN 28013 head; torispherical heads, shallower than semi-ellipsoidal ones, with C = 0.30939 + 1.7197 (Rk − 0.06 Do)/Di − 0.16116 t/Do + 0.98997 (t/Do)² (ASME) and C = 0.37802 + 0.05073 t/Do + 1.3762 (t/Do)² (DIN 28011), where t is the wall thickness and Rk the knuckle radius (after Wiencke 2009, Doane 2007, Ludwig 1997)
- Neutrium, Volume and wetted area of partially filled vertical vessels: the cylindrical body (π/4)D²h; a semi-ellipsoidal bottom head D³C(π/24)(3(h/z)² − (h/z)³) with z the dish depth and C = 0.5 for the ASME 2:1 head; a hemispherical head (πh²/3)(3R − h)
- Wolfram MathWorld, Conical Frustum: V = πh(R₁² + R₁R₂ + R₂²)/3, applied from the outlet up to the level reached in a cone-bottom tank
- Wolfram MathWorld, Ellipse: the area of an ellipse with semi-axes a and b is πab, and the change of coordinates x′ = (b/a)x turns the ellipse into a circle of radius b — so every slice across an elliptical section is the circle's slice stretched by a/b, and a part-filled ellipse holds the circle's segment times width over height
- NIST Special Publication 811, Appendix B.8: gallon (U.S.) = 3.785 412 E−03 m³, and gallon [Canadian and U.K. (Imperial)] = 4.546 09 E−03 m³ — the two gallons the rows below state together with litres and cubic metres
- Derived on this page: a tank with straight vertical sides holds its plan area times the depth (the box, and the upright ellipse at πab), and a flat-sided oval is a rectangle between two half-circles of the smaller dimension, filled piece by piece with the circular segment above; the tests check both by integrating the width of each horizontal slice
Inputs used
- Tank Shape
- Cylinder standing upright (water, rainwater and storage tanks)
- Inside Diameter
- 6 ft
- Straight Side Height
- 6.5 ft
- Ends of the Cylinder
- Flat
- Inside Diameter
- 4 ft
- Straight Barrel Length
- 8 ft
- Ends of the Cylinder
- Flat
- Inside Length
- 4 ft
- Inside Width
- 3.5 ft
- Inside Height
- 3.5 ft
- Inside Width Across
- 5 ft
- Inside Height
- 3.5 ft
- Inside Length
- 6.5 ft
- Inside Length of the Oval
- 5 ft
- Inside Width of the Oval
- 3.5 ft
- Inside Height
- 5 ft
- Inside Width (side to side)
- 27 in
- Inside Height (bottom to top)
- 44 in
- Inside Length (end to end)
- 60 in
- Inside Diameter of the Barrel
- 5 ft
- Straight Barrel Height
- 5 ft
- Cone Height
- 2 ft
- Outlet Diameter at the Bottom of the Cone
- 4 in
- Liquid Depth
- 24 in
- Lowest Draw-Off Height
- 0 in
Intermediate steps
- Capacity when full
- 1,374.79 gal
- Space left above the liquid
- 951.78 gal
- Liquid above the lowest draw-off
- 423.01 gal
- Depth as a share of the inside height
- 30.77 %
- Contents as a share of capacity
- 30.77 %
- Inside height, bottom to top
- 6.5 ft
- Contents in litres (L)
- 1,601.28 L
- Contents in cubic metres (m³)
- 1.6 m³
- Contents in US gallons (gal)
- 423.01 gal
- Contents in imperial gallons (imp gal)
- 352.23 imp gal
- Capacity in litres (L)
- 5,204.16 L
- Capacity in cubic metres (m³)
- 5.2 m³
- Capacity in US gallons (gal)
- 1,374.79 gal
- Capacity in imperial gallons (imp gal)
- 1,144.76 imp gal
Confidence note: Standing upright on a flat bottom, the tank has the same cross-section at every level, so depth and contents rise together and a dipstick marked in equal steps reads true from bottom to top.
What this calculation does not cover
- This is geometry, not gauging. A real tank bulges, dents, sits out of level, carries sludge and has fittings inside it, and none of that is in the arithmetic. For fuel accounting, custody transfer or anything a regulator reads, the governing figure is the tank's own calibrated strapping table or the maker's capacity chart.
- Every dimension wanted is an INSIDE one. A plastic, bunded or insulated tank's walls are thick enough that outside measurements overstate the capacity, and a double-skinned tank's outer shell can be a good deal larger than the vessel holding the liquid.
- Depth is measured from the lowest point inside. A tank out of level has a different depth at each end, and a reading taken from the ground, a plinth or the outside of a cradle is not the inside depth; measure at the middle, or at both ends and compare.
- Dished ends are taken as the 2:1 ellipsoidal head, a quarter of the diameter deep, and both ends of a cylinder as the same kind. A DIN 28013 head is about as deep and holds almost as much. Most torispherical (flanged-and-dished) heads, the ASME and DIN 28011 kinds among them, are shallower and hold less — by Neutrium's coefficients for a thin wall, roughly 62% and 76% of a 2:1 head of the same diameter — and their exact volume needs the wall thickness and the knuckle radius, which this page does not ask for. A tank with a flat bottom and a domed top is outside the model too; a maker's drawing governs.
- The two ovals are different shapes. An elliptical tank is a true ellipse in section; a flat-sided oval has straight sides between round ends and holds more for the same width and height. Tanks sold as oval can be either, so check which you have before trusting either figure.
- Nothing here is converted to mass. Oils, fuels and chemicals differ in density, and density moves with temperature, so the same depth can be a different weight on a hot afternoon than on a cold morning.
- Capacity is the volume the shell encloses, not a fill target. Tanks are filled short of it to leave room for expansion and for the overflow and vent to work, and the working volume of a rainwater or process tank sits between its overflow and its lowest draw-off.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-10-05 · v1.0.0
Regulatory standards & verification citations6
- Neutrium, Volume and wetted area of partially filled horizontal vessels: the barrel as a circular segment, L(R² cos⁻¹((R − h)/R) − (R − h)√(2Rh − h²)); a hemispherical head πh²(3R − h)/6; a semi-ellipsoidal head D³C(π/12)(3(h/D)² − 2(h/D)³) with C = 1/2 for the ASME 2:1 head, whose depth is a quarter of the diameter, and C = 0.49951 + 0.10462 t/Do + 2.3227 (t/Do)² for a DIN 28013 head; torispherical heads, shallower than semi-ellipsoidal ones, with C = 0.30939 + 1.7197 (Rk − 0.06 Do)/Di − 0.16116 t/Do + 0.98997 (t/Do)² (ASME) and C = 0.37802 + 0.05073 t/Do + 1.3762 (t/Do)² (DIN 28011), where t is the wall thickness and Rk the knuckle radius (after Wiencke 2009, Doane 2007, Ludwig 1997)
- Neutrium, Volume and wetted area of partially filled vertical vessels: the cylindrical body (π/4)D²h; a semi-ellipsoidal bottom head D³C(π/24)(3(h/z)² − (h/z)³) with z the dish depth and C = 0.5 for the ASME 2:1 head; a hemispherical head (πh²/3)(3R − h)
- Wolfram MathWorld, Conical Frustum: V = πh(R₁² + R₁R₂ + R₂²)/3, applied from the outlet up to the level reached in a cone-bottom tank
- Wolfram MathWorld, Ellipse: the area of an ellipse with semi-axes a and b is πab, and the change of coordinates x′ = (b/a)x turns the ellipse into a circle of radius b — so every slice across an elliptical section is the circle's slice stretched by a/b, and a part-filled ellipse holds the circle's segment times width over height
- NIST Special Publication 811, Appendix B.8: gallon (U.S.) = 3.785 412 E−03 m³, and gallon [Canadian and U.K. (Imperial)] = 4.546 09 E−03 m³ — the two gallons the rows below state together with litres and cubic metres
- Derived on this page: a tank with straight vertical sides holds its plan area times the depth (the box, and the upright ellipse at πab), and a flat-sided oval is a rectangle between two half-circles of the smaller dimension, filled piece by piece with the circular segment above; the tests check both by integrating the width of each horizontal slice
Cite this page
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