CE ChemicalEngineers.in
Process & Storage Engineering Tool

Vertical Tank Volume & Calibration Calculator

Calculate exact liquid volume, mass, fill percentage and calibration data for vertical cylindrical tanks with flat, conical, hemispherical, 2:1 ellipsoidal, or torispherical top and bottom heads — in any combination.

Any top/bottom head combination Cone-bottom & flat-bottom supported Handles empty, partial & full conditions Calibration table + CSV export Level transmitter mA output
Calculator

Tank Geometry & Liquid Inputs

Shell Geometry
Heads

Ellipsoidal default depth = 25% of diameter (2:1). Torispherical default: 100% crown, 6% knuckle (ASME F&D). Conical: specify height or half-apex angle — the other is computed automatically.

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 vertical cylindrical tank or vessel with any top and bottom head configuration — flat, conical, hemispherical, 2:1 ellipsoidal, or torispherical — by integrating the true cross-sectional area of the shell and each head along the liquid height, correctly handling liquid that sits entirely within the bottom head, within the shell, or within the top head.

It is built for process engineers, plant operators, 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 calibration (strapping) table for a vertical vessel with a cone bottom, dished bottom, or flat bottom.

Typical Industrial Applications

Storage & feed tanks

Vertical bulk storage tanks, day tanks, and feed tanks for chemicals, water, or intermediates.

Batch reactors & process vessels

Stirred-tank reactors and general process vessels with dished or conical bottoms.

Surge vessels

Vertical knockout drums and surge tanks between process units.

Cone-bottom tanks

Solids-handling and slurry tanks that rely on a conical bottom for complete drainage.

Vertical tanks used across chemical storage, water treatment, food and beverage, and pharmaceutical processing all share the same underlying geometry challenge: liquid volume is not a simple linear function of height once the head shapes are included, and accurate inventory tracking directly affects mass balances, batch sizing, and safe operating margins.

Guide

How to Use This Calculator

  1. Enter shell geometry. Input the internal diameter and the straight (tangent-to-tangent) shell height.
  2. Select head types. Choose the top and bottom head types independently — for example, an ellipsoidal top with a conical bottom. Adjust depth/crown/knuckle/cone parameters if needed.
  3. Set the liquid level. Enter the liquid height from the absolute bottom of the tank (including any bottom head), 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 for a spreadsheet or DCS.
  7. Configure the level transmitter. Enter LRV and URV to see the 4–20 mA output for the current level, or back-calculate level from a known mA value.
Worked example: A tank with 2 m internal diameter, 4 m tangent-to-tangent shell height, a 2:1 ellipsoidal top head, and a conical bottom head with a 60° included angle, filled to a liquid height of 2.0 m from the absolute bottom, gives a total volume of roughly 13.7 m³ and a liquid volume that includes the fully flooded cone bottom plus part of the straight shell. Enter these values above to see the exact computed results, including the level transmitter output.
Engineering Reference

Mathematical Formulas Used in This Calculator

All formulas below are the exact expressions implemented in this page's JavaScript. Because the tank is vertical, every horizontal cross-section is a full circle, so head volumes are found by integrating the disk area π·r(z)² along the head's axial profile (Simpson's rule), rather than the circular-segment integration needed for horizontal tanks.

V_cap(s) = ∫₀ˢ π·r_local(t)² dt
s
Distance travelled into the head from its lowest point, in the direction of rising liquid
r_local(t)
Head radius at distance t from its lowest point (tip-first for a bottom head, base-first for a top head)

Engineering significance: because a vertical tank's cross-section is always a full circle, no circular-segment geometry is required — only the disk area at each height, integrated numerically with Simpson's rule (220+ intervals).

Hemispherical: r(zz) = √(R² − zz²), a = R
Ellipsoidal (2:1 default): r(zz) = R·√(1 − (zz/a)²), a = k·D (default k = 0.25)
Torispherical: a = L − √((L−r_k)² − (R−r_k)²)
Conical: r(zz) = R·(1 − zz/a), a = R / tan(θ) or a given directly
zz
Axial distance from the base (shell junction, r=R) toward the tip (r=0)
a
Total head depth / cone height
θ
Cone half-apex angle (included angle = 2θ)
L, r_k
Torispherical crown radius (default 1.00·D) and knuckle radius (default 0.06·D)

For a conical head, either the cone height or the half-apex angle can be entered — the calculator solves the other from R = a·tan(θ). Assumption: standard axisymmetric head geometry, tangent knuckle-to-crown blending for torispherical heads.

V_shell = π·R²·L
V_total = V_cap,bottom(a_bottom) + π·R²·L + V_cap,top(a_top)
R
Internal shell radius
L
Straight (tangent-to-tangent) shell height
If h ≤ a_bottom: V_liquid = V_cap,bottom(h)
If a_bottom < h ≤ a_bottom+L: V_liquid = V_cap,bottom(full) + π·R²·(h − a_bottom)
If h > a_bottom+L: V_liquid = V_cap,bottom(full) + π·R²·L + V_cap,top(h − a_bottom − L)
h
Liquid height measured from the absolute bottom of the tank (0 ≤ h ≤ total tank height, clamped for overflow)

This piecewise formula is what allows the calculator to correctly handle liquid confined entirely to the bottom head, entirely within the shell, or extending into the top head, as well as fully empty and fully flooded (overflow-clamped) conditions.

Fill % = 100 · V_liquid / V_total
m = ρ · V_liquid , W = m · g (g = 9.80665 m/s²)
mA = 4 + 16 · (H − LRV) / (URV − LRV), clamped to [4, 20]
H = LRV + (mA − 4)/16 · (URV − LRV)

Assumption: linear 4–20 mA level transmitter with no damping, offset, or non-linearity error.

Assumptions

Engineering Assumptions

  • Tank axis is perfectly vertical; no tilt or out-of-plumb condition is accounted for.
  • Shell and heads are geometrically ideal (no dents, corrosion allowance, or fabrication tolerance).
  • Internals (baffles, coils, agitators, dip pipes, nozzles) are not subtracted from the liquid volume.
  • Liquid is a single homogeneous phase with a flat, undisturbed free surface.
  • Straight shell height 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.
  • Conical heads are right circular cones, symmetric about the tank axis.
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.
  • Assumes the conical bottom fully drains to a point apex; sump or drain-nozzle geometry at the very apex is not separately modeled.
  • 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