Equation guide
Tank volume and liquid-level equations
Tank capacity is calculated from internal geometry. Partial volume depends on the vessel orientation: liquid depth changes volume linearly in a vertical cylinder or rectangular tank, but not in a horizontal cylinder because the wetted cross-sectional area is a circular segment.
Use measured internal dimensions whenever possible. Nominal tank size, wall thickness, dished heads, internal equipment, tilt, and a manufacturer’s strapping table can make actual capacity differ from ideal geometry.
Vertical cylindrical tank
V = πr²h- r = inside radius
- h = liquid height
Full capacity uses the total inside height in place of liquid height.
Rectangular tank
V = L × W × h- L = inside length
- W = inside width
- h = liquid height
Horizontal cylindrical tank
V = L[r² cos⁻¹((r − h) ÷ r) − (r − h)√(2rh − h²)]L is cylinder length, r is inside radius, and h is liquid depth from the bottom. The inverse cosine must be evaluated in radians.
Percent full
Percent full = Liquid volume ÷ Total capacity × 100Remaining volume equals total capacity minus calculated liquid volume.
Common volume conversions
1 ft³ = 7.48052 US gal | 1 m³ = 1,000 LKeep every dimension in one length unit before calculating cubic volume.
Worked example: vertical cylindrical tank
A 10 ft inside-diameter tank with 20 ft total height contains 12 ft of liquid.
Tank volume FAQs
Why is a horizontal cylinder not linear with liquid depth?
Near the bottom and top, a small depth change covers less cross-sectional area than the same change near the center. The circular-segment equation accounts for that changing geometry.
Should I enter outside or inside dimensions?
Use inside dimensions. Outside diameter and nominal dimensions overstate available liquid volume unless wall thickness and vessel construction are accounted for.
Does the calculator include dished or conical heads?
No. It calculates ideal cylinders and rectangular tanks. Use the manufacturer’s strapping table or a head-specific calculation when the ends materially affect capacity.
Can this replace a certified tank chart?
No. It is a field-estimation tool. Custody transfer, regulated inventory, and high-accuracy applications should use a certified strapping table or approved measurement method.
Field caution: Never use calculated volume as the sole control for overfill protection, confined-space entry, or other safety-critical work.