Tank Volume Calculator
The horizontal-cylinder law done honestly — total capacity, partial fill by the circular segment, and the dip ladder that proves depth never maps to volume.
Tank Volume Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Plain horizontal cylinders — capsule heads and cone bottoms are their own geometry.
- Centerline dip assumed; end dips read the curve wrong.
- No temperature-density correction.
In short: A 120-in tank on a 48-in bore holds 940.03 gallons full, 470.01 at half depth — the one depth that is exact — and 237.18 gallons at 14.4-in depth, just 25.23% of capacity. Depth lies; the segment formula does not.
Formula
full = π r² L ÷ 231
partial: V = ½ r² (θ − sin θ) L, θ = 2 acos((r − d) ÷ r)
half depth → θ = π → exact half
1 gal = 231 in³; water = 8.34 lb/gal
[('segment', 'the circle sliced by the waterline'), ('θ', '2 acos((r−d)÷r) — the wet angle, radians'), ('25.23%', 'volume at 30% of bore — depth lies'), ('231', 'in³ per US gallon, exact')]
Worked Example
- Measure the inside bore and straight shell length.
- Dip the tank at centerline for true depth.
- Full capacity: πr²L ÷ 231.
- Partial: segment law at the dip; never multiply by depth fraction.
- Check the dip ladder before trusting any gauge.
48-in bore × 120 in: 940.03 gal full; 470.01 at the 24-in dip (exact half); 237.18 gal at the 14.4-in dip = 25.23% — a quarter of the water at less than a third of the bore.
Strengths & Limits Of This Model
Where this engine is strong
- Segment law computed live, including the dip ladder
- The exact-half fact stated and provable
- Saddle-load weight at full and at dip
Where it stops
- Cylindrical shells only
- No strapping-chart output
Practical Use Cases
Heating oil
Dip-to-gallons without the paper chart.
Farm and sprayer tanks
Partial loads by dip stick.
Process tanks
Ullage and freeboard checks.
Cisterns
Stored water at any depth.
Saddle design
Full-load weight at 8.34 lb/gal.
Methodology & Editorial Standards
Full capacity is the cylinder law on inside dimensions (πr²L, in³ ÷ 231). Partial fill is the circular-segment law with the wet angle θ = 2 acos((r − d)÷r), never a depth-fraction multiplication. The dip ladder recomputes the segment at every 10% of bore live, so the page itself demonstrates the nonlinearity it preaches. Depth above the crown refused as a spill; zero depth is an honest empty. Weight at 8.34 lb/gal.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Tank Volume Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
How do I calculate a partially filled horizontal tank?
With the circular segment: V = ½ r² (θ − sin θ) L, where θ = 2 acos((r − d) ÷ r) and d is the liquid depth. Multiplying full volume by the depth fraction is the classic error — it is wrong at every depth except half.
Is half full really half the volume?
Yes — the waterline through the centerline makes θ = π, and the segment becomes exactly half the circle. A 940.03-gallon tank holds 470.01 gallons at the half-depth dip.
My gauge says 30% — how much is really in it?
30% of the bore is 25.23% of the volume on a 48-in tank: 237.18 gallons of 940.03. The gap peaks near the quarter marks; the dip ladder card shows it at every ten percent.
What about a vertical cylinder tank?
Vertical cylinders fill linearly — depth fraction IS volume fraction: V = πr²H with the liquid depth as H. No segment law needed; that is the easy case.
How many gallons in a rectangular tank?
L × W × H in inches ÷ 231, linear in fill depth like the vertical cylinder. IBC totes and stock tanks are the everyday cases.
What does the water in my tank weigh?
8.34 lb per gallon: the 940.03-gallon example load is 7,839.85 lb — saddles, pads and foundations are designed for that number, not the gallon count.
Should I fill a tank to 100%?
No — leave 5-15% freeboard for thermal expansion and slosh. The dip ladder’s upper rows are where expansion headroom lives, not product.
Can I trust my dip stick?
Only at the half mark. A stick marked in even tenths of the bore reads true at 50% and drifts as much as 5 points of volume near the quarters — the dip ladder card shows the true fraction at every tenth.