Vertical Cylinder Tank Volume Calculator

This calculator works out the volume of a vertical cylindrical tank from the diameter (or radius) and height you enter, returning the result in gallons, liters, cubic feet, and cubic meters. You input the tank’s inside dimensions and the liquid depth (if not full), and it gives the filled volume and the total capacity. The math uses the standard cylinder formula, so you can verify every result by hand.

Formula

The volume of a vertical cylinder is the area of the circular base times the height (or liquid depth). The base area is π times the radius squared, which is also π/4 times the diameter squared.

V = (π/4) × D² × h

• V = volume (cubic feet, cubic meters, liters, gallons, etc.)
• D = inside diameter of the tank (same unit as h)
• h = height of the liquid (or full tank height for capacity)
• π ≈ 3.14159

For a full tank, replace h with the total tank height H. To convert cubic feet to US gallons, multiply by 7.48052; to liters, multiply cubic feet by 28.3168 (or work directly in meters: 1 m³ = 1000 L).

Worked Example

Using the default values from the calculator: diameter D = 5 ft, liquid depth h = 4 ft, tank height H = 6 ft.

1. Base area = (π/4) × D² = (3.14159/4) × 25 = 0.7854 × 25 = 19.635 ft²
2. Liquid volume = 19.635 × 4 = 78.54 ft³
3. Total capacity = 19.635 × 6 = 117.81 ft³
4. Liquid volume in gallons = 78.54 × 7.48052 = 587.5 US gal
5. Liquid volume in liters = 78.54 × 28.3168 = 2224 L

The calculator’s headline answer is 78.54 ft³ for the liquid volume, matching the hand calculation. The total capacity is 117.81 ft³ (about 881 US gallons).

When to Use a Vertical Cylinder Calculator

Vertical cylindrical tanks are common for water storage, fuel oil, chemical storage, and many industrial processes. Use this calculator when you need to know:

• How much liquid is currently in the tank (based on a dipstick reading)
• How much the tank can hold when full (for sizing or shipping)
• How much space a tank will occupy (for installation planning)
• How to calibrate a level sensor or sight glass

The same formula applies to any vertical cylinder—a propane tank, a rain barrel, a brewing fermenter, or a pressure vessel. Just be sure to measure the inside dimensions, not the outside, unless you want the outer volume including wall thickness.

How to Measure a Tank Correctly

Accuracy starts with the measurements. Follow these steps for reliable results:

1. Measure the inside diameter at the widest point (for a perfectly cylindrical tank, any cross-section works; for a tank with slight bulging, take several measurements and average them).
2. Measure the height from the bottom (inside) to the top edge (inside). For liquid depth, measure from the bottom to the liquid surface—not to the top of the tank.
3. Use the same unit for both dimensions. If you mix feet and inches, convert first (12 inches = 1 foot).
4. If the tank has a dished or conical bottom, the simple cylinder formula underestimates the volume. In that case, add the volume of the bottom shape separately (e.g., a cone: V = (1/3)πr²h).

For a tank that is not perfectly vertical (slightly tilted), the liquid surface is not parallel to the bottom, so the simple formula gives only an approximation. For large tilt angles, use a horizontal cylinder calculator or a strapping table.

Common Mistakes and How to Avoid Them

• Using outside dimensions: Wall thickness reduces the inside volume. For a steel tank with ¼-inch walls, the diameter error is 0.5 inches—small, but it adds up on large tanks.
• Mixing units: If you enter diameter in feet and height in inches, the result is meaningless. Always convert to one unit.
• Forgetting to subtract the bottom dish: Many vertical tanks have a curved or sloped bottom. The cylinder formula assumes a flat bottom.
• Using radius instead of diameter: The formula uses D². If you have the radius, use V = πr²h. Doubling the radius is not the same as using diameter—it gives 4 times the correct volume.
• Rounding too early: If you round π to 3.14, the error is about 0.05%. That’s fine for most purposes, but for a 10,000-gallon tank, it’s 5 gallons off. Use 3.14159 or the calculator’s value.

Limits of the Simple Formula

The formula V = (π/4)D²h is exact only for a right circular cylinder with flat ends, vertical orientation, and a liquid surface parallel to the bottom. Real tanks often deviate:

• Dished heads (top/bottom): Common on pressure vessels. The additional volume can be 5–10% of the cylindrical portion.
• Conical bottoms: Used in some storage tanks to aid draining. The cone volume is one-third of the cylinder volume of the same height.
• Elliptical heads: The volume of each head is roughly 0.13 × D³ for a 2:1 ellipsoidal head.
• Thermal expansion: Liquids expand when heated. A tank filled to the brim at 60°F may overflow at 80°F. Always leave headroom (ullage).
• Internal fittings: Agitators, baffles, heating coils, and dip tubes displace liquid. Subtract their volume for precise inventory.

For these cases, use a tank strapping table from the manufacturer or a more advanced calculator that accounts for head shapes.

Units and Conversions

The calculator returns cubic feet, gallons, and liters. If you need other units, use these conversion factors:

• 1 cubic foot = 7.48052 US gallons = 6.22884 imperial gallons
• 1 cubic meter = 1000 liters = 264.172 US gallons
• 1 liter = 0.264172 US gallons = 0.219969 imperial gallons
• 1 US gallon = 231 cubic inches = 0.133681 ft³

For a quick mental check: a 5-foot diameter tank, 1 foot deep holds about 147 gallons (π/4 × 25 × 7.48 ≈ 147). So 4 feet deep gives roughly 588 gallons—matching the example.

Safety and Accuracy Notes

When measuring a real tank, follow basic safety practices:

• Do not open a tank that contains flammable, toxic, or pressurized contents. Use a dipstick or ultrasonic level sensor from the outside.
• If you must enter a confined space, follow proper permit procedures and use gas detection.
• For fuel or chemical tanks, always leave expansion space. Never fill to 100%—typically 90–95% max.
• Check the tank’s calibration chart if one exists; it may be more accurate than a simple formula.
• For legal custody transfer (buying/selling fuel), use a certified strapping table, not a generic calculator.

This calculator is for planning and estimation. It does not replace professional calibration or regulatory compliance.

Frequently Asked Questions

How do I calculate the volume of a vertical cylinder tank in gallons?

Use the formula V = (π/4) × D² × h, where D is the inside diameter and h is the liquid depth (both in feet). The result is in cubic feet. Multiply by 7.48052 to get US gallons. For example, a 4-foot diameter tank with 3 feet of water holds (π/4 × 16 × 3) = 37.7 ft³ × 7.48 = 282 gallons.

What is the difference between total capacity and liquid volume?

Total capacity is the volume when the tank is filled to the very top (using the full tank height H). Liquid volume is what’s actually in the tank (using the measured liquid depth h). For a partially filled tank, liquid volume is less than capacity. The calculator shows both so you can see how much room is left.

Can I use this calculator for a horizontal cylinder tank?

No. Horizontal tanks have a different formula because the liquid surface is not parallel to the ends—the cross-section is a circular segment. For a horizontal tank, use a dedicated horizontal cylinder calculator or a strapping table. Using the vertical formula for a horizontal tank will be inaccurate unless the tank is completely full or empty.

Why does my dipstick reading not match the calculator?

Possible reasons: the tank has a dished or sloped bottom, the tank is tilted, the dipstick is not vertical, or the tank has internal fittings. Also, check that you measured the inside diameter correctly (not the outside) and that you used the same units. If the tank is old, it may have dents or bulges that change the volume.

How accurate is this calculator for a real tank?

For a perfectly cylindrical tank with flat ends, the formula is exact. For real tanks with dished heads, the error can be 2–10% depending on head shape. For inventory purposes, that may be acceptable. For custody transfer or safety-critical applications, use a certified calibration chart.

What if my tank has a cone bottom?

Add the cone volume to the cylinder volume. The cone volume is (1/3) × π × r² × h_cone, where r is the radius and h_cone is the cone height. For example, a 5-foot diameter tank with a 2-foot cone bottom adds (1/3 × π × 2.5² × 2) = 13.09 ft³, about 98 gallons. The calculator does not include this automatically.

Related

• Square Foot Calculator with Height: Volume in Sq Ft
• Square Footage Calculator: How to Measure Any Room
• Square Footage Calculator With Height

in d | Tank diameter | ft | 5 | 0
in h | Liquid depth | ft | 4 | 0
in H | Tank height | ft | 6 | 0
out vol_ft | Liquid volume | ft³ | (pi/4)*d^2*h | 2
out cap_ft | Total capacity | ft³ | (pi/4)*d^2*H | 2
out vol_gal | Liquid volume | US gal | ((pi/4)*d^2*h)*7.48052 | 1
out vol_l | Liquid volume | L | ((pi/4)*d^2*h)*28.3168 | 0