🔷 Trapezoid Tank Calculator
Calculate volume and fill level of trapezoidal tanks and troughs
Enter Tank Dimensions
Fill: 62.5% (hf = 5 cm)
📊 Trapezoid Tank Results
Top Width (a)
12 cm
Bottom Width (b)
6 cm
Tank Height (H)
8 cm
Fill Height (hf)
5 cm
Length (L)
20 cm
Fill Volume
781.25 cm³
Total Capacity
1,440 cm³
Fill Percentage
54.3%
📝 Step-by-Step Solution
Given: a = 12 cm, b = 6 cm, H = 8 cm, L = 20 cm, hf = 5 cm
Width at fill height: w(hf) = b + (a-b) × (hf/H) = 6 + 6 × (5/8) =
9.75 cm
Partial fill area: A = ((b + w(hf)) / 2) × hf = ((6 + 9.75) / 2) × 5
= 39.375 cm²
Fill volume: V = A × L = 39.375 × 20 = 787.5 cm³
Total capacity = ((a+b)/2) × H × L = 9 × 8 × 20 = 1,440 cm³
📐 Trapezoid Tank Formulas
Cross-section Area: A = ((a + b) / 2) × h
Full Tank Volume: V = ((a + b) / 2) × h × L
Width at height hf: w = b + (a - b) × (hf / H)
Partial Fill: V = ((b + w(hf)) / 2) × hf × L
Understanding Trapezoid Tanks
🔷 Trapezoidal Prism
Cross-section is a trapezoid. Common in troughs, hopper tanks, and V-shaped containers. Two parallel sides of different widths.
📏 Width at Height
Width changes linearly with height. w(hf) = b + (a-b)×(hf/H). Narrower at bottom, wider at top (or vice versa).
🌊 Partial Fill
Forms a smaller trapezoid. Calculate width at fill level, then use trapezoid area formula for the filled portion.
⚖️ Non-Linear Fill
Volume not proportional to height. Wider at top means more volume per height unit near the top.
Frequently Asked Questions
What is the formula for trapezoid tank volume?
V = ((a + b) / 2) × h × L. Average of parallel sides times height
times length. Cross-section area times length.
How do I calculate partial fill volume?
Find width at fill height first. w = b + (a-b)×(hf/H). Then V =
((b + w) / 2) × hf × L.
What is width at fill height?
Linear interpolation between top and bottom. w(hf) = b + (a-b) ×
(hf/H). At hf=0: w=b. At hf=H: w=a.
Is half height equal to half volume?
No, not for trapezoids. Due to changing width, volume is
non-linear with height. Wider end has more volume per unit height.
What if top is narrower than bottom?
Still works, swap a and b. Or use formula as-is—negative (a-b)
handles inverted trapezoids.
How do I find fill height from volume?
Quadratic equation. Our calculator uses numerical methods to solve
for hf given V.
What is a trapezoidal trough?
Open-top container. Used for animal feeding, water channels, and
industrial processes. Same formula applies.
Can I use this for V-shaped tanks?
Set b = 0. Triangle cross-section is special case of trapezoid.
Formula still works.
How accurate for real tanks?
Exact for true trapezoids. Real tanks may have rounded corners,
welds, or slopes affecting actual volume.
What is the difference from rectangular tank?
Rectangle: a = b. When parallel sides are equal, trapezoid becomes
rectangle. Volume = a × h × L.
How do I convert to gallons?
1 gallon = 3,785.41 cm³. Our calculator can output in gallons,
liters, or other units automatically.
What is cross-section area?
A = ((a + b) / 2) × h. The 2D trapezoid shape. Multiply by length
for volume.
How do I find required length for target volume?
L = V / A. Divide target volume by cross-section area. Our "Find
Length" mode calculates this.
What about sloped ends?
More complex calculation. This calculator assumes flat ends.
Sloped ends require additional formulas.
Why are trapezoid tanks common?
Easy gravity flow. V-bottom helps contents drain. Common in
hoppers, feeders, and processing equipment.
What is the perimeter of the cross-section?
P = a + b + 2s. Where s = slant height = √(h² + ((a-b)/2)²). For
material calculations.
Can I calculate surface area?
SA = 2×A + perimeter×L. Two trapezoid ends plus four rectangular
sides (two may be parallelograms).