🛢️ Barrel Calculator 2026
Calculate volume, capacity, and dimensions of barrels and casks
Presets:
Enter Barrel Dimensions
r = end radius, R =
middle radius, h = height
📊 Results
End Radius (r)
29.2 cm
Middle Radius (R)
32.4 cm
Height (h)
89 cm
Volume
225.6 L
Surface Area
1.89 m²
Bilge Diameter
64.8 cm
📝 Step-by-Step Solution
Given: r = 29.2 cm, R = 32.4 cm, h = 89 cm
Using barrel approximation formula (parabolic profile):
V = (πh/15) × (2R² + r² + 2Rr + r²) ≈ (πh/12) × (2R² + r²)
V = (π × 89 / 12) × (2 × 1049.8 + 852.6) = 225,643 cm³
V = 225,643 cm³ = 225.6 Liters
📐 Barrel Volume Formulas
Approximate: V = (πh/12) × (2R² + r²)
Exact (parabolic): V = (πh/15) × (3R² + 4Rr + 8r²/3)
Average cylinder: V = π × ((R+r)/2)² × h
Where: R = middle radius, r = end radius, h = height
Understanding Barrel Geometry
🛢️ Barrel Shape
Curved cylinder wider in the middle (bilge) than at the ends. Traditional cooperage design. Makes rolling easier and distributes pressure.
📏 Key Dimensions
R = bilge (middle) radius, r = end radius, h = height/stave length. Bilge is always larger than ends.
🍷 Standard Sizes
Wine barrel: 225L (Bordeaux), Whiskey: 200L, Oil barrel: 159L (42 US gal), Beer keg: 50L.
📐 Approximation
Profile is parabolic or elliptical. Formulas use approximations. Actual volume may vary 1-3% based on exact curve.
Frequently Asked Questions
What is the volume formula for a barrel?
V = (πh/12) × (2R² + r²) is a common approximation. R = middle
radius, r = end radius, h = height. Accounts for curved sides.
How many gallons in a standard oil barrel?
42 US gallons (159 liters). This is the petroleum industry
standard. Also equals 35 imperial gallons.
What is a wine barrel capacity?
225 liters (59.4 US gallons) for Bordeaux barrique. Other sizes:
Burgundy 228L, American 200L, Sherry 500L.
What is the bilge of a barrel?
The widest part in the middle. Barrels curve outward at the
center. Bilge diameter = 2R (middle radius × 2).
Why are barrels curved?
Easier to roll and maneuver. Curved shape also distributes
internal pressure, makes staves easier to bend during construction.
How do I measure a barrel?
Measure end diameter, bilge diameter, and height. Divide diameters
by 2 for radii. Height is the stave length (top to bottom).
What is a whiskey barrel size?
53 US gallons (200 liters) for American standard barrel. Bourbon
must use new charred oak. Scotch often uses ex-bourbon barrels.
How accurate is the barrel formula?
Within 1-3% for typical barrel shapes. Actual curve profile
affects accuracy. Use exact measurements for precision.
What is a barrel vs cask?
Interchangeable terms. "Cask" often used for smaller or
wine/spirits. "Barrel" common in oil industry. Both are curved wooden vessels.
How do I convert barrel volume to gallons?
1 liter = 0.264 US gallons. Or: 1 liter = 0.22 imperial gallons.
Our calculator handles conversions automatically.
What is the surface area of a barrel?
Approximation: 2πh(R+r)/2 + 2πr². Curved surface plus two end
circles. Used for coating or heat transfer calculations.
What is a beer keg capacity?
50 liters (13.2 US gal) for standard half-barrel. Mini keg: 5L.
Full barrel: 117L (31 gal). Quarter barrel: 58.7L.
How do I find missing radius from volume?
Rearrange formula. If you know volume and one radius, solve for
the other. Generally requires numerical methods for exact solution.
What materials are barrels made from?
Oak is traditional for wine/spirits. Steel for oil. Plastic or
stainless for modern food. Oak adds flavor and allows micro-oxygenation.
What is the difference between R and r?
R = middle (bilge) radius, the widest point. r = end
radius, top and bottom. R is always larger than r for a proper barrel shape.
Can I use this for cylindrical tanks?
If R = r, it becomes a cylinder. Formula simplifies to πr²h. For
slight bulge, use barrel formula for better accuracy.
How accurate is this calculator?
Uses standard parabolic approximation. Accuracy depends on how
well the actual barrel matches this profile. Generally within 2%.