Excel calculator for measuring volume and displacement with a cup or bucket

It's easy to measure the volume of a fluid sample or the volumetric displacement of an irregularly-shaped object if you have access to a "graduated cylinder" of the appropriate size. Unfortunately, graduated cylinders, especially big ones, are hard to come by. Measuring cups for cooking can work for small amounts of liquid and small dunked-objects, but they're usually not marked in fine enough increments to provide scientific precision.

Other mundane vessels such as cups and buckets can be used to measure displacement pretty well if you don't mind doing a little extra math and measurement. The purpose of this post is to simplify that math and share a tool that will do it for you. At the end of the post I share a story of how a student and I applied this technique to answer an ecological question. 

The Math Part: There's a formula for the volume of a cylinder (V = πr²h) that makes it easy to relate fluid volume to the level of fluid in a cylindrical container. In the formula, r is the radius of the cylinder and h is the height. Most cups and buckets are not true cylinders, though. They're usually wider at the top than at the base, so technically they are a truncated cone or "frustum" shape. The formula for the volume of a frustum is V = (1/3)π(R²+Rr+r²)h where R is the bigger radius of the top and r is the smaller radius of the bottom. Another thing that's tricky about a frustum compared to a true cylinder is that its vertical height (h) is shorter than the length along the wall (w), which complicates measurement. Luckily, the relationship between h and w can be calculated by substituting the relevant measures into the Pythagorean theorem for right triangles, a² + b² = c² -> (R-r)² + h² = w² then solving for h.

The Practical Approach: Follow this step by step guide and use the Microsoft Excel calculator tool embedded and linked below to turning a frustum shaped cup or bucket into a useful measuring container. The calculator file has two worksheets- "Template" is a blank version with no measurements added yet, and "Example" is filled out already with approximate dimensions of a hardware store bucket. 

Step 1) Measure the inner diameter at the wider (top) of the vessel, which we'll call "D." Half that diameter will give us the radius of the top of the vessel, "R." If you enter the value for D the calculator will fill in the value for R. 

Step 2) Measure the inner diameter of the bottom of the vessel, which we'll call "d". You might have to measure the outer diameter of the bottom of the vessel and subtract 2x the wall thickness to get the inner diameter. Half of d will give us the radius of the inside bottom of the vessel, "r." If you enter the value for d the calculator will fill in the value for r. 

Step 3) Measure the inside wall length from top to bottom, which we'll call "W." Enter that in the calculator. The calculator will now give you the total volume of the vessel in cubic mm, cubic cm, and liters. You can tweak the file if you need volume expressed in different units. 

Step 4) Put the vessel down on a flat, even surface and partially fill it with liquid. Add enough liquid to cover the object(s) you're going to dunk in it, but not so much that it will overflow when you dunk the object(s). It shouldn't matter what liquid you use, but water is nice. 

Step 5) Measure the distance from the rim of the vessel to the surface of the liquid and enter it in column L. We're calling that value "B" because it's the before dunking measurement. 

Step 6) Dunk whatever you need to measure the volume of in the liquid and measure the distance from the rim of the vessel to the surface of the liquid again. Enter it in column M. We're calling this value "A" because it's the after dunking measurement. If the thing you're measuring the displacement of floats you might have to push it down or weigh it down in a bag to get it all the way under. Just be careful that you account for the volume of whatever other objects you're using to sink the object of interest. Also make sure there aren't any air bubbles trapped in the thing you're sinking, unless you want the air pockets included in the volume. Note that the fluid displacement method won't work if the thing you dunk dissolves in the fluid, because dissolved matter won't displace as much fluid as solid matter.

Step 7) Once you've filled in all the yellow boxes the calculator should be giving you accurate values for volume of the fluid, volume of the fluid + object, and volume of the object. 

This is the calculator- It should work online but it will probably be less annoying if you download it. 

How my student used it: In fall 2025, one of my undergraduate research interns used an earlier version of this bucket displacement method to determine how much space is occupied by the plants in dry detention ponds with different management styles. Her results showed that even though it LOOKS like the plants in a natural meadow or wetland occupy a lot of 3d space, the volume that they actually take up is negligible. I.e., the added water storage capacity you get by mowing a dry detention pond is less than 1 vertical millimeter and doesn't justify the loss of plant habitat and ecosystem services that occurs when you mow. 

For the sake of completeness, I shall end this post with a classic meme image of a southern elephant seal (Mirounga leonina) with a bucket.