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Loading...We understand that it isn’t very easy to estimate how many gallons or litres your container can hold.
That’s why we built our online tank volume calculator. 🤘
Keep reading to see how using our capacity calculator makes calculating the volume of your tank easy.
But first…
Contents:
Calculate the volume of liquid your container can hold by entering your dimensions in metric units (centimeters or meters) or imperial units (yards, feet or inches).
Our tool estimates the total tank volume and liquid capacity using the below formulas:
The total volume of a horizontal cylindrical tank is calculated by using the formula:
$$Volume = \pi × Radius^2 × Length$$
Where
$$Radius = {Diameter \over 2}$$
The total volume of a vertical cylindrical tank is calculated by using the formula:
$$Volume = \pi × Radius^2 × Height$$
Where
$$Radius = {Diameter \over 2}$$
The total volume of a rectangular tank is calculated by using the formula:
$$Volume = Length × Width × Height$$
The total volume of a capsule tank is calculated by using the formula:
$$Volume= \pi × Radius^2 × \biggl(Side\,Length+ {4 × Radius \over 3}\biggr)$$
Where
$$Radius = {Diameter \over 2}$$
The total volume of a capsule tank is calculated by using the formula:
$$Volume= \pi × Radius^2 × \biggl(Side\,Height+ {4 × Radius \over 3}\biggr)$$
Where
$$Radius = {Diameter \over 2}$$
The total volume of an oval tank is calculated by using the formula:
$$Volume = Length × (π × Radius^2 + Width × Y)$$
Where
$$Radius = {Width \over 2}$$
and
$$Y = Height – Width \quad if\,Height > Width$$
$$Y = Width – Height \quad if\,Width > Height$$
The total volume of an oval tank is calculated by using the formula:
$$Volume = Height × (π × Radius^2 + Width × Y)$$
Where
$$Radius = {Width \over 2}$$
and
$$Y = Length – Width \quad if\,Length > Width$$
$$Y = Width – Length \quad if\,Width > Length$$
The total volume of a cone bottom tank is calculated by using the formula:
$$Volume = Volume\,Cylinder + Volume\,Frustrum$$
Where
$$Volume\,Cylinder = \pi × Top\,Radius^2 × Cylinder\,Height$$
And
$$Volume\,Frustrum = {1 \over 3} × \pi × Frustrum\,Height × (Top\,Radius^2 + Bottom\,Radius^2 + Top\,Radius × Bottom\,Radius)$$
With
$$Top\,Radius = {Top\,Diameter \over 2}$$
and
$$Bottom\,Radius = {Bottom\,Diameter \over 2}$$
Our tank volume calculator also has an option for a tank that is only partially filled.
The formulae start to become more complicated when we look at tanks that are only partially filled, so make sure you check the values carefully – using our calculator can help you simplify the process! 😉
Below are the formulae the calculator uses to work out the volume of water or fuel in a partially filled tank:
The volume of water, filled to a certain depth, is given by:
$$Filled\,Volume = {1 \over2} × Radius^2 × (x – sin\,x ) × Length$$
Where
$$x = 2 × cos^{-1} \biggl({Radius – Filled\,Depth \over Radius}\biggr)$$
and
$$Radius = {Diameter \over 2}$$
$$Filled\,Volume = \pi × Radius^2 × Filled\,Depth$$
Where
$$Radius = {Diameter \over 2}$$
$$Filled\,Volume = Length × Width × Filled\,Depth$$
$$Filled\,Volume = {1 \over 2} × Radius^2 × (x – sin\,x) × Length + (Length × Filled\,Depth × (Width – Height))$$
$$x = 2 × cos^{-1} \biggl({Radius – Filled\,Depth \over Radius}\biggr)$$
and
$$Radius = {Width \over 2}$$
$$Filled\,Volume = {1 \over 2} × Radius^2 × (x – sin\,x) × Length$$
Where
$$x = 2 × cos^{-1} \biggl({Radius – Filled\,Depth \over Radius}\biggr)$$
and
$$Radius = {Width \over 2}$$
$$Filled\,Volume = {1 \over 2} × \pi × Radius^2 × Length + (Filled\,Depth – Radius) × Length × Width$$
Where
$$Radius = {Width \over 2}$$
$$Filled\,Volume = Total\,Liquid\,Capacity – Empty\,Portion$$
Where
$$Empty\,Portion = \pi × Radius^2 × Length – {1 \over 2} × Radius^2 × (x – sin\,x) × Length$$
and
$$x = 2 × cos^{-1} \biggl({Radius – Filled\,Depth \over Radius}\biggr)$$
and
$$Radius = {Width \over 2}$$
$$Filled\,Volume = Filled\,Cylinder + Filled\,Spherical\,Ends$$
Therefore
$$Filled\,Volume = {1 \over 2} × Radius^2 × (x – sin\,x) × Length + {\pi × Filled\,Depth^2 \over 3} × (1.5 × Diameter – Filled\,Depth)$$
Where
$$x = 2 × cos^{-1} \biggl({Radius – Filled\,Depth \over Radius}\biggr)$$
and
$$Radius = {Diameter \over 2}$$
$$Filled\,Depth < {Diameter \over 2}$$
then:
$$Filled\,Volume = {\pi × Filled\,Depth^2 \over 3} × (1.5 × Diameter – Filled\,Depth)$$
$${Diameter \over 2} < Filled\,Depth < {Diameter \over 2} + Length$$
then:
$$Filled\,Volume = {2 \over 3} × \pi × Radius^3 + \pi × Radius^2 × {Filled\,Depth – Diameter \over 2}$$
$${Diameter \over 2} + Length < Filled\,Depth$$
then:
$$Filled\,Volume = Total\,Capsule\,Volume – Spherical\,Cap$$
So
$$Filled\,Volume = Capsule\,Volume – {1 \over 3} × \pi × Filled\,Depth^2 × (1.5 × Diameter – (Length + Diameter – Filled\,Depth))$$
$$Filled\,Depth < Frustum\,Height$$
Then, the total volume of the water contained in the tank is given by calculating the volume of the frustum filled:
$$Filled\,Volume = {1 \over 3} × \pi × Frustum\,Height × (R^2 + R × Bottom\,Radius + Bottom\,Radius^2 )$$
Where
$$Bottom\,Radius = {Bottom\,Diameter \over 2}$$
and
$$R = {1 \over 2} × Top\,Diameter × {Filled\,Depth + Z \over Frustum\,Height+Z}$$
Where
$$Z = Missing\,Cone\,Height$$
$$Frustum\,Height < Filled\,Depth$$
Then
$$Filled\,Volume = Cylindrical\,Filled\,Volume + Frustrum\,Volum$$
Where
$$Cylindrical\,Filled\,Volume = \pi × Radius^2 × (Filled\,Depth – Frustum\,Height)$$
Confused? 🤔
See below for four full examples showing in detail how our calculator works.
Otherwise, simply enter your measurements for your container in our tank size calculator!
✅ Cylindrical Oil Tank
$$Volume = \pi × Radius^2 × Length$$
Where
$$Radius = {Diameter \over 2}$$
Therefore
$$Volume = \pi × {5 ft \over 2}^2 × 7\,yd = 412.3\,ft^3 = 3084\,US\,Gal$$
Now, let’s say we filled the cylindrical tank to a height of 2 feet. The total water in the tank is calculated by:
$$Filled\,Volume = {1 \over2} × Radius^2 × (x – sin\,x ) × Length$$
Where
$$x = 2 × cos^{-1} \biggl({Radius – Filled\,Depth \over Radius}\biggr) = 2 × cos^{-1} \biggl({2.5\,ft – 2\,ft \over 2.5\,ft}\biggr) = 156.9$$
and
$$Radius = {Diameter \over 2} = {5\,ft \over 2} = 2.5\,ft$$
Therefore
$$Filled\,Volume = {1 \over2} × 2.5\,ft^2 × (156.9 – sin\,156.9 ) × 7\,yd = 154\,ft^3 = 1152.1\,US\,Gal$$
✅ Rectangular Fuel Tank
$$Volume = Length × Width × Height = 2\,ft × 4\,ft × 10\,in = 6.667\,ft^3 = 1.187\,bbl$$
Now, let’s say that we filled the fuel tank to a height of 3 inches.
To calculate the total volume of the liquid the calculator would do the following operations:
$$Filled\,Volume = Length × Width × Filled\,Depth = 2\,ft × 4\,ft × 3\,in = 2\,ft^3 = 14.96\,US\,Gal$$
✅ Horizontal Capsule Tank
$$Volume= \pi × Radius^2 × \biggl(Length+ {4 × Radius \over 3}\biggr)$$
Where
$$Radius = {Diameter \over 2}$$
Therefore
$$Volume= \pi × \biggl({10\,in \over 2}\biggr)^2 × \biggl(30\,in + {4 \over 3} × {10\,in \over 2}\biggr) = \pi × 5\,in^2 × \biggl(30\,in + {20\,in \over 3}\biggr) = 2879.793\,in^3 = 47.2\,l$$
Therefore, my tank measures approximately 2880 cubic inches and I can fill it with 47.2 liters of water.
Now, let’s say that I want to fill the tank to a depth of 3 inches.
To calculate the total amount of liquid in the tank, the calculator would do the following calculations:
$$Filled\,Volume = {1 \over 2} × Radius^2 × (x – sin\,x) × Length + {\pi × Filled\,Depth^2 \over 3} × (1.5 × Diameter – Filled\,Depth)$$
Where
$$x = 2 × cos^{-1} \biggl({Radius – Filled\,Depth \over Radius}\biggr) = 2 × cos^{-1} \biggl({5\,in – 3\,in \over 5\,in}\biggr) = 132.84$$
and
$$Radius = {10\,in \over 2} = 5\,in$$
Therefore
$$Filled\,Volume = {1 \over 2} × 5\,in^2 × (132.84 – sin\,132.84) × 30\,in + {\pi × 3\,in^2 \over 3} × (1.5 × 10\,in – 3\,in) = 0.409\,ft^3 = 3.06\,US\,Gal$$
✅ Horizontal Oval Tank
$$Volume = Length × (π × Radius^2 + Width × Y)$$
Where
$$Radius = {Width \over 2}$$
and
$$Y = Height – Width \quad if\,Height > Width$$
$$Y = Width – Height \quad if\,Width > Height$$
Therefore
$$Volume = 7\,ft × (π × 50\,cm^2 + 100\,cm × (4\,ft – 100\,cm)) = 2.803\,yd^3 = 2143.411\,litres$$
Note that we use Y = Height – Width because height (4 ft = 121cm) is larger than 100 cm.
Now, let’s say I have filled the tank with water to a depth of 1.5 ft.
The calculator works out the total volume of water by doing the following calculations:
$$Filled\,Volume = {1 \over 2} × Radius^2 × (x – sin\,x) × Length + (Length × Filled\,Depth × (Width – Height))$$
Where
$$x = 2 × cos^{-1} \biggl({Radius – Filled\,Depth \over Radius}\biggr) = 2 × cos^{-1} \biggl({50\,cm – 1.5\,ft \over 50\,cm}\biggr) = 170.2$$
and
$$Radius = {Width \over 2} = {100\,cm \over 2} = 50\,cm$$
Therefore
$$Filled\,Volume = {1 \over 2} × 50\,cm^2 × (170.2 – sin\,170.2) × 7\,ft + (7\,ft × 1.5\,ft × (100\,cm – 4\,ft)) = 26.37\,ft^3 = 197.25\,US\,Gallons$$
At this point, it’s likely that you are asking the following question:
The best part of our online calculator is that it takes care of this for you! 😉
Looking through our examples, perhaps you noticed that we changed units between feet, centimeters, inches and so on, e.g. in example 2:
$$Volume = Length × Width × Height = 2\,ft × 4\,ft × 10\,in = 6.667\,ft^3 = 1.187\,bbl$$
We can do this because our calculator is able to do the conversions for you, making it far easier for you!
For each measurement there are multiple options that are available to use. For example, length can be calculated in terms of feet (ft), inches (in), yards (yd), meters (m) or centimeters (cm).
The calculator takes care of this by using the following conversions:
$$1\,foot = 12\,inches = 0.33\,yards = 30.48\,centimeters = 0.3048\,meters$$
$$1\,ft^3 = 1728\,in^3 = 0.037\,yd^3 = 28316.8\,cm^3 = 0.0283168\,m^3$$
Note that the default value for all lengths is inches, tank volume is cubic inches and liquid capacity is US gallons.
Each of these can be changed by pressing the arrows next to the unit measurements and selecting the correct unit from the drop down options.
We think that our tank volume calculator is an effective and powerful online tool. It makes calculating the volume of your tank very easy! 😊
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