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Horizontal Tank Volume Calculator

Computes the liquid volume in a horizontal cylindrical tank from its diameter, length and the measured liquid depth, using the circular-segment area for flat ends and adding two spherical-cap segments for hemispherical ends, plus total capacity, fill percentage and remaining ullage.

When to use

You need to convert a dipstick or sight-glass reading on a horizontal fuel, water, oil or chemical tank into litres or gallons, or want the tank's total capacity.

Do not use when: The tank stands vertically or is rectangular (volume is simply area × depth; use cylinder or rectangular-prism), has dished or elliptical (2:1) heads, or is not level.

Formula

r = diameter_m / 2, h = liquid_level_m; segment area A = r² · acos((r − h) / r) − (r − h) · √(2·r·h − h²); cylinder liquid volume = A × length_m; hemispherical ends add π·h²·(3·r − h)/3 (a spherical cap of height h; the two half-spheres together form one sphere); total = π·r²·length_m (+ 4/3·π·r³ for hemispherical ends); fill_percent = liquid / total × 100

Exact geometry for a level tank with a true cylindrical shell; wall thickness, internal fittings and dished (torispherical or 2:1 elliptical) heads are not modelled, so hemispherical is an upper bound for domed heads. Volumes are geometric and do not account for thermal expansion of the liquid.

Inputs

Parameter	Type	Unit	Required	Description
`diameter_m`	number	m	yes	Internal diameter of the cylindrical shell in metres (1 ft = 0.3048 m, 1 in = 0.0254 m). Range: > 0, ≤ 100
`length_m`	number	m	yes	Length of the straight cylindrical section in metres, excluding the end caps. Range: > 0, ≤ 1000
`liquid_level_m`	number	m	yes	Depth of liquid measured vertically from the bottom of the tank, 0 to diameter_m. Range: ≥ 0, ≤ 100
`end_type`	enum: flat \| hemispherical		default flat	Shape of the two end caps.

Outputs

Output	Type	Unit	Description
`liquid_volume_m3`	number	m³	Volume of liquid at the given level.
`liquid_volume_liters`	number	L	Liquid volume in litres (1 m³ = 1000 L).
`liquid_volume_gal_us`	number	gal (US)	Liquid volume in US gallons (1 gal = 3.785411784 L).
`total_volume_m3`	number	m³	Volume of the full tank including the end caps.
`total_volume_liters`	number	L	Full-tank capacity in litres.
`total_volume_gal_us`	number	gal (US)	Full-tank capacity in US gallons.
`fill_percent`	number	%	liquid volume / total volume × 100.
`empty_volume_liters`	number	L	Volume still available: total minus liquid.
`level_percent`	number	%	liquid_level_m / diameter_m × 100 (the height fraction, which is not the volume fraction).

Example

2 m diameter, 5 m long, 0.5 m of liquid, flat ends: {"diameter_m":2,"length_m":5,"liquid_level_m":0.5,"end_type":"flat"} → {"liquid_volume_m3":3.0709,"liquid_volume_liters":3070.9,"liquid_volume_gal_us":811.3,"total_volume_m3":15.708,"total_volume_liters":15708,"fill_percent":19.55,"empty_volume_liters":12637,"level_percent":25}

3 m diameter, 6 m shell, 2 m of liquid, hemispherical ends: {"diameter_m":3,"length_m":6,"liquid_level_m":2,"end_type":"hemispherical"} → {"liquid_volume_m3":40.5082,"liquid_volume_liters":40508.2,"total_volume_m3":56.5487,"fill_percent":71.63,"level_percent":66.67}

GET https://tttkmbb.com/api/v1/calculate/horizontal-tank-volume?diameter_m=2&length_m=5&liquid_level_m=0.5&end_type=flat

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/horizontal-tank-volume (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/horizontal-tank-volume · Markdown: https://tttkmbb.com/engineering/horizontal-tank-volume.md · JSON definition: https://tttkmbb.com/engineering/horizontal-tank-volume.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="horizontal-tank-volume"
OpenAPI operationId: calculate_horizontal_tank_volume
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Circular segment (reference)
Wikipedia – Spherical cap (reference)

FAQ

Why is a half-full dipstick reading not 25 % of the volume at a quarter of the diameter?

The cross-section is a circle, so the volume per centimetre of depth is smallest near the bottom and top and largest at the centre; at 25 % of the diameter a flat-ended tank holds only about 19.6 % of its volume.

Does length_m include the end caps?

No. Enter the straight shell length; hemispherical heads add their own volume automatically (each head extends by the tank radius).

My tank has dished (torispherical) heads.

Dished heads hold less than hemispherical ones (roughly 8–10 % of the cylinder volume per pair of 2:1 elliptical heads on a tank with L = 2D). Use flat and hemispherical as lower and upper bounds, or the manufacturer's strapping chart.

Related calculators

Cylinder Calculator — Volume and surface area of a full cylinder.
Circle Sector and Segment Calculator — Area of the circular sector and segment used here.
Pipe Flow Calculator (Hazen–Williams) — Flow and pressure drop in the pipe filling or draining the tank.