Vessel Volume & Level Calculation

Q: How do I calculate vessel volume from liquid level?

Enter internal Diameter (D), straight Length/Height (L), select head types for both ends, choose orientation, and input level (H). The calculator converts H → Volume instantly.

Q: Which head type should I select if drawings aren’t clear?

If unknown, ASME F&D (f=1, k=0.06) is a practical default in many plants.

Q: Do jackets or limpet coils change the capacity?

External jackets do not change internal volume; limpet coils usually don’t either unless they intrude inside.

Q: Does the agitator (anchor, PBT, hydrofoil) affect level-to-volume?

If the agitator/shaft/baffles intrude inside, they reduce capacity slightly.

Q: The tank is slightly tilted—will calibration be wrong?

Yes, even small slope/tilt shifts the level-to-volume curve.

Q: Can I mix different head types on top and bottom (or left/right)?

Yes—select per-end head types.

Vessel volume & level calculation ensures that every millimetre of liquid height converts into an accurate capacity value—across vertical and horizontal tanks. SV Industries provides a practical, engineer-friendly approach so your operators get trustworthy inventory numbers, faster batches, and cleaner audits.

🎯 What this covers

Works for common head geometries: ellipsoidal (2:1), hemispherical, torispherical (ASME F&D / standard / 0.8:0.1), and flat.
Handles both orientations with correct level reference: vertical (from bottom apex) and horizontal (0…D).
Unit flexibility: mm, m, inch—with consistent conversions.

vessel volume & level calculation

Accurate level-vs-volume for vertical/horizontal vessels. Units: mm, m, inch, ft. Chart + CSV export.

Inputs

Orientation

Units

Diameter, D (internal)

Straight length/height, L (internal)

Bottom head

Bottom head type

Top head

Top head type

Vertical: H measured from bottom apex. Horizontal: H range 0…D (e.g., D=1000 ⇒ 10% = 100 mm).

Filled level, H

Calibration step

Live visual preview

Results

Bottom/Left depth a₁

—

Top/Right depth a₂

—

Total level range

—

Solver

Closed-form

Total volume

—

Filled volume

—

Orientation

Vertical

Level %	Level (unit)	Volume (m³)	Volume (L)	Volume (gal, US)

Need more accuracy? Tilt/slope (horizontal) or dead-volume/min-drain modeling — contact us to enable.

Quick Start (2-minute Guide)

Follow these fast steps to get accurate level → volume in minutes. No CAD, no spreadsheets—just enter your geometry and download the calibration.

🧭 Choose Orientation
Select Vertical (H measured from bottom apex) or Horizontal (H ranges 0…D).
Tip: Horizontal tanks: 10% level = 0.1 × D (e.g., D=1000 → 100 mm).
📐 Set Units
Pick mm, m, or inch. The calculator converts consistently—no rounding surprises across results.
⌀ Enter Internal Dimensions
- Diameter (D) — internal only
- Straight length/height (L) — shell length excluding heads
  If you’re sizing a new build, see our vessel options: Reactor Vessel or SS Jacketed Vessel.
🧩 Select Bottom & Top Head Types
Choose from Ellipsoidal (2:1), Hemispherical, Torispherical (ASME F&D / Standard / 0.8/0.1), or Flat.
Note: Head geometry affects dish depth and total capacity—match your fabrication drawing.
📏 Enter Filled Level (H)
- Vertical: H from the bottom apex upward.
- Horizontal: H from lowest point; valid range 0…D.
🔁 Pick Calibration Step
Select 5% or 10% to generate a clean Level–Volume table suitable for SOPs and ERP upload.
▶️ Review Live Visual & Results
The preview shows liquid fill (SV brand color), while outputs display Filled Volume, Total Volume, and a Level–Volume chart.
Need custom validation for your tank? Contact Us.
⬇️ Export
- CSV for spreadsheets/ERP
- Print/PDF for QA files and audits
  Want examples? Browse our latest posts in the Blog.

Pro tip: Mixing or heat-transfer constraints in real plants (coils, jackets, baffles) can change effective working capacity. Explore Limpet Coil Reactors to align calculation with actual process hardware.

Supported Head Types

Right head selection = right capacity. Our calculator models the most-used geometries exactly—so your level-to-volume stays reliable across builds and standards.

Head Type	Depth (a)	Geometry / Parameters	Typical Use	Why it helps	Explore
Ellipsoidal (2:1)	`a = D / 4`	2:1 ellipse; R/r not required	Reactors, jacketed vessels	Balanced capacity without excessive height; good for agitator clearances	Reactor Vessel · SS Jacketed
Hemispherical (“Spherical” Head)	`a = D / 2`	Half-sphere cap; R/r not required	Higher pressure / thermal cycling	Best stress distribution; maximizes end-cap volume	Process Reactor
Torispherical (ASME F&D) f=1 · k=0.06	`R = f·D = D` `r = k·D = 0.06D` `a = R − √((R−r)² − (A−r)²)`, A=D/2	Crown + knuckle per ASME	Industry default for many vessels	Predictable fabrication; balanced height & capacity	Reactor Vessel
Torispherical (Standard F&D) f=1 · k=0.1	`R = D` `r = 0.1D` `a` as per formula above	Gentler knuckle radius	Hygiene + fabrication friendly	Smoother transitions may improve local stresses & cleanability	SS Jacketed
Torispherical (F&D) f=0.8 · k=0.1	`R = 0.8D` `r = 0.1D` `a` increases due to tighter crown	Designs needing deeper dish	Modifies end-volume & headroom; model captures exact change	Industrial Reactor
Flat	`a = 0`	Flat plate; R/r not applicable	Atmospheric/low-pressure, removable covers	Simple fabrication; lowest added head volume	Products

Vertical vs Horizontal — Level Reference

⬆️Vertical

Reference point: bottom head apex (deepest internal point).

H_total = a_bottom + L + a_top (dish depths + straight length; all values are internal).

0 ≤ H ≤ a_bottom — filling the bottom head.
a_bottom < H ≤ a_bottom + L — cylindrical shell region.
a_bottom + L < H ≤ H_total — top head (complement).

Sight-glass or transmitter zero should align with the apex datum to avoid offset errors.

Considering a new build? Explore Reactor Vessels and SS Jacketed Vessels.

⬅️➡️Horizontal

Reference point: the lowest internal point of the shell.

Valid H range: 0 … D (diameter). Example: if D = 1000 mm, then 10% level = 100 mm.

H = 0 — empty; H = D/2 — ~50% cylinder area (heads added via integration).
H = D — full (cylinder + both heads at full).
Transmitter “0%” at the drain datum; “100%” at top-of-ID. Record actual D during commissioning.

Validation & Sample Cases

🧪Benchmark A — Vertical (ASME F&D heads both ends)

Inputs: D = 1000 mm, L = 2000 mm; Bottom head = Top head = Torispherical (ASME F&D, f=1, k=0.06)
Expected dish depth (each): a ≈ 169.34 mm
Total level range: H_total = a_bottom + L + a_top ≈ 2338.68 mm
Total volume: ≈ 1.7328 m³ (±0.2%)
Sanity: 100% level ≈ 2338.7 mm; total volume matches.

📦Benchmark B — Horizontal (Flat ends; pure cylinder sanity)

Inputs: D = 1000 mm, L = 2000 mm; Left/Right heads = Flat

Cylinder volume (exact): A = D/2 = 500 mm → V_cyl = π·A²·L = π·500²·2000 mm³ ≈ 1.570796 m³

Level H (mm)	Expectation	Volume (m³)
0	Empty	0
500 (D/2)	~Half cylinder area	≈ 0.785398
1000 (D)	Full cylinder	≈ 1.570796

🔵Benchmark C — Vertical (Hemispherical heads both ends)

Inputs: D = 1000 mm, L = 2000 mm; Bottom/Top = Hemispherical
Dish depth (each): a = D/2 = 500 mm
Per-head volume (exact): V_head = (2/3)·π·A³ = (2/3)·π·500³ mm³ ≈ 0.261799 m³
Total volume: V ≈ V_cyl + 2V_head ≈ 1.570796 + 0.523599 = 2.094395 m³
Total level range: H_total = 500 + 2000 + 500 = 3000 mm

🔍How to cross-check quickly

Level datums: Vertical → bottom apex; Horizontal → 0…D (lowest to highest internal point).
Units & rounding: Keep all inputs in one unit; export CSV and verify with your ERP sheet.
Head selection: Match fabrication drawing (ASME F&D vs Standard vs 0.8/0.1) to avoid skew.
Visual preview: Shape & meniscus should reflect orientation/heads; compare with vessel photos in the Gallary.

Need validation against P&IDs or as-built drawings? We can align calibration to your Reactor Vessel or SS Jacketed Vessel and provide signed QA PDFs — Contact Us.

Vessel Volume & Level Calculation

🎯 What this covers