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Process & Storage Engineering Tool

Horizontal Tank Volume & Calibration Calculator

Calculate exact liquid volume, mass, fill percentage and calibration data for horizontal cylindrical tanks with flat, hemispherical, 2:1 ellipsoidal, or torispherical heads — in any combination of the two ends.

Any head combination Numerical integration, not approximations Calibration table + CSV export Level transmitter mA output Metric & imperial units
Calculator

Tank Geometry & Liquid Inputs

Shell Geometry
Heads

Ellipsoidal default depth = 25% of diameter (standard 2:1). Torispherical default: 100% crown radius, 6% knuckle radius (ASME F&D).

Liquid
Display Units
Alarm & Operating Levels (height, same unit as liquid level)
Level Transmitter (4–20 mA)

Tank Visualization

Liquid LL / HH L / H Normal

Results

Calibration Table

Fill %HeightVolumeMassWeight (N)
About

What This Calculator Does

This tool computes the liquid inventory of a horizontal cylindrical tank or vessel of any head configuration — flat, hemispherical, 2:1 ellipsoidal, or torispherical — by numerically integrating the true cross-sectional geometry of the shell and each head along the liquid level, rather than relying on lookup charts or single-head-type approximations.

It is built for process engineers, plant operators, terminal and storage staff, and instrumentation engineers who need to convert a measured liquid height into volume, mass, or a 4–20 mA transmitter signal, or who need a full calibration (strapping) table for a horizontal vessel.

Typical Industrial Applications

Fuel & chemical storage

Diesel, gasoline, solvent, and bulk chemical horizontal storage tanks at plants, depots, and fuel stations.

Process vessels

Feed drums, surge vessels, knockout drums, and horizontal reactors in refineries and chemical plants.

Terminal & logistics

Tank truck offloading tanks, rail-car receiving tanks, and intermediate bulk storage.

Inventory & custody transfer

Daily inventory reconciliation, mass-balance checks, and calibration verification against strapping tables.

Accurate inventory calculation matters because horizontal tanks have a non-linear relationship between liquid height and volume — a small error in head-volume assumptions compounds into significant inventory discrepancies, especially near the bottom and top of the vessel where the heads contribute proportionally more.

Guide

How to Use This Calculator

  1. Enter shell geometry. Input the internal diameter and the straight (tangent-to-tangent) shell length, choosing appropriate units for each.
  2. Select head types. Choose the left and right head types independently. If you pick ellipsoidal or torispherical, adjust the depth/crown/knuckle ratios if your vessel differs from the ASME standard defaults shown.
  3. Set the liquid level. Enter the liquid height from the bottom of the tank, or drag the level slider.
  4. Enter density. Provide the liquid density (or specific gravity) to get mass and weight results.
  5. Read the results panel. Total volume, liquid volume, empty volume, fill %, mass, and weight update instantly, alongside the scaled visualization.
  6. Generate a calibration table. Pick an increment and export it as CSV, or copy it directly for use in a spreadsheet or DCS configuration.
  7. Configure the level transmitter. Enter LRV and URV to see the corresponding 4–20 mA output for the current level, or enter a known mA value to back-calculate the level.
Worked example: A tank with 2 m internal diameter, 6 m tangent-to-tangent shell length, and two standard torispherical (ASME F&D) heads, filled to a liquid height of 1.0 m (50% of diameter) with a liquid of density 850 kg/m³, gives a total volume of roughly 20.0 m³, a liquid volume of roughly 10.0 m³ at the exact half-full point, and a liquid mass of roughly 8,500 kg. Enter these values above to see the exact computed results.
Engineering Reference

Mathematical Formulas Used in This Calculator

All formulas below are the exact expressions implemented in this page's JavaScript. Head volumes are found by numerically integrating (Simpson's rule) the circular-segment area of each head's true radial profile along its axial depth — this correctly handles the compound spherical-crown/toroidal-knuckle shape of torispherical heads instead of using a fixed-percentage approximation.

A(r, h) = r²·cos⁻¹((r−h)/r) − (r−h)·√(2rh − h²)
A(r,h)
Area of the circular segment wetted by liquid, for a circle of radius r
r
Local circle radius (shell radius, or head profile radius at a given axial position)
h
Liquid height measured from the bottom of that local circle (0 ≤ h ≤ 2r)

Engineering significance: this is the exact closed-form area of a circular segment, used for both the cylindrical shell cross-section and every axial slice of each head. Limitation: undefined derivative exactly at h=0 and h=2r is handled by boundary clamping (returns 0 or πr²).

V_shell(h) = A(R, h) · L
R
Internal shell radius
L
Straight (tangent-to-tangent) shell length

Assumption: perfectly cylindrical shell with horizontal axis and no internals or dead volume.

V_head(h) = ∫₀ᵃ A( r(z), clamp(h − R + r(z), 0, 2r(z)) ) dz
a
Total axial depth of the head (0 for flat)
r(z)
Head radial profile at axial position z from the tangent line
clamp(x,0,2r)
Restricts the local liquid height to a physically valid range

Evaluated numerically with Simpson's rule (240+ intervals). Engineering significance: this is a general method valid for any axisymmetric head profile, giving accurate results without a separate closed-form derivation per head type.

Hemispherical: r(z) = √(R² − z²), 0 ≤ z ≤ R
Ellipsoidal (2:1 default): r(z) = R·√(1 − (z/a)²), a = k·D (default k = 0.25)
Torispherical: a = L − √((L−r_k)² − (R−r_k)²)
L
Crown (dish) radius, default 1.00·D
r_k
Knuckle radius, default 0.06·D (ASME F&D)
k
User-adjustable ellipsoidal depth ratio (% of diameter)

The torispherical profile is modeled as a toroidal knuckle band blending tangentially into a spherical crown; the transition point is solved from the tangency condition between the two circles in the meridian plane. Assumption: standard axisymmetric F&D-type geometry; non-standard flanged/dished proportions can be entered via the crown and knuckle ratio fields.

V_total = A(R,2R)·L + V_head,left(2R) + V_head,right(2R)
V_liquid = V_shell(h) + V_head,left(h) + V_head,right(h)
Fill % = 100 · V_liquid / V_total
m = ρ · V_liquid , W = m · g (g = 9.80665 m/s²)
ρ
Liquid density
m
Liquid mass
W
Liquid weight (force)
mA = 4 + 16 · (H − LRV) / (URV − LRV), clamped to [4, 20]
H = LRV + (mA − 4)/16 · (URV − LRV)
LRV / URV
Lower / upper range values of the transmitter, in height units

Assumption: linear 4–20 mA level transmitter with no damping or sensor offset error.

Assumptions

Engineering Assumptions

  • Tank axis is perfectly horizontal; no trim, tilt, or settlement is accounted for.
  • Shell and heads are geometrically ideal (no dents, corrosion allowance, or fabrication tolerance).
  • Internals (baffles, coils, agitators, nozzles) are not subtracted from the liquid volume.
  • Liquid is a single homogeneous phase with a flat, undisturbed free surface.
  • Straight shell length is the true tangent-to-tangent dimension, excluding head depth.
  • Torispherical heads follow standard ASME flanged-and-dished (F&D) proportions unless the crown and knuckle ratios are changed.
Limitations

Limitations & Intended Use

  • Not a substitute for a certified strapping/calibration table for custody-transfer or fiscal metering purposes.
  • Does not account for thermal expansion of the liquid or the vessel shell.
  • Does not model vessel internals, insulation thickness, or external jacket volume.
  • Torispherical geometry assumes standard tangent knuckle-to-crown blending; heavily non-standard dish shapes should be verified independently.
  • Intended for engineering estimation, design checks, and operational reference — always verify against the manufacturer's vessel data sheet or a certified gauge table for critical applications.
FAQ

Frequently Asked Questions