Determining how many regular size marshmallows fit in a cup requires some quick calculations based on the size of both marshmallows and the cup. On average, regular marshmallows have a diameter of about 1 inch and a volume of around 1 cubic inch. The size of a standard measuring cup is usually 8 fluid ounces or 16 fluid ounces. By estimating the amount of empty space between marshmallows and accounting for how they settle towards the bottom of the cup, we can come up with a reasonable range for how many fit in a cup.
Average Size of Regular Marshmallows
Regular sized marshmallows are typically about 1 inch (2.54 cm) in diameter. Some brands may be slightly larger or smaller, but 1 inch is a good standard size to use for calculations. Marshmallows are roughly spherical. Using the standard formula to calculate the volume of a sphere, we find that each marshmallow takes up about 1 cubic inch (16.4 cubic cm) of space.
V = 4/3 π r3
Where V is volume, π is 3.14, and r is radius.
For a 1 inch diameter marshmallow:
r = 0.5 inch
V = 4/3 π (0.5 inch)3 = 0.5236 cubic inches ≈ 1 cubic inch
This will be useful for estimating how many marshmallows can fit in a given container volume.
Standard Measuring Cup Sizes
Measuring cups come in a variety of sizes, but two of the most common are:
- 8 fluid ounce (237 ml) cup
- 16 fluid ounce (473 ml) cup
Since marshmallows are solid rather than liquid, we need to consider what the actual empty interior volume of the cups are. Cups are usually about 4 inches tall. Taking the radius of each size cup into account, we can estimate the empty interior volumes:
8 fluid ounce cup:
Radius = 1.75 inches
Interior volume = π r2 h
= 3.14 x (1.75 in)2 x 4 in
= 97 cubic inches
16 fluid ounce cup:
Radius = 2.25 inches
Interior volume = π r2 h
= 3.14 x (2.25 in)2 x 4 in
= 191 cubic inches
This gives us the estimated empty volumes we have available to work with for each cup size.
How Marshmallows Fit Together
Marshmallows are compressible and can smush together to some degree. When packing marshmallows into a container, they won’t maintain a perfect cubic arrangement. We need to account for gaps that will occur between marshmallows as they are pressed together.
Experiments by enthusiasts packing marshmallows into various containers show that you can usually achieve a packing density of around 50-55% with marshmallows. That means about 50-55% of the container volume will be occupied by marshmallows, and the rest will be empty space between them.
This packing density takes into account the marshmallows settling down into the bottom of the container as they are added. Shaking or agitating the container can compact them further. For our estimates, we’ll use 50% packing density to be on the conservative side.
Calculating Marshmallows in 8 Ounce Cup
For an 8 fluid ounce measuring cup with an estimated interior volume of 97 cubic inches:
At 50% packing density, marshmallows will occupy about 48 cubic inches.
With each regular marshmallow occupying 1 cubic inch, this means the cup can hold an estimated 48 marshmallows.
Calculating Marshmallows in 16 Ounce Cup
For a 16 fluid ounce measuring cup with an estimated interior volume of 191 cubic inches:
At 50% packing density, marshmallows will occupy about 95 cubic inches.
With each regular marshmallow occupying 1 cubic inch, this means the cup can hold an estimated 95 marshmallows.
Range of Marshmallows in Cup
Summarizing our calculations:
- 8 fluid ounce cup holds approximately 48 regular marshmallows
- 16 fluid ounce cup holds approximately 95 regular marshmallows
Of course, results will vary slightly in practice based on how uniformly the marshmallows are packed and how much they are compressed into the cup. But this gives us a reasonable ballpark range to expect for how many will fit.
Factors Affecting Results
There are a few factors that can influence these estimates to some degree:
- Exact cup size – We used estimated average sizes, but exact dimensions can vary.
- Marshmallow size – Using mini marshmallows would change the numbers.
- Marshmallow freshness – Stale marshmallows are firmer and may not compact as well.
- Packing method – How much effort is used to pack them can change density.
- Cup shape – Conical cups may compact better than cylindrical.
But the calculated ranges should still give a good ballpark estimate for most standard size cups and regular marshmallows.
Ways to Estimate Further
If you wanted to determine a more precise number experimentally, a few options include:
- Measuring interior dimensions of the exact cup used.
- Taking a sample size of marshmallows and calculating average volume.
- Trying a small test batch in the cup and extrapolating from that.
- Using volume displacement in a graduated cylinder.
But for most purposes our estimates based on standard sizes and packing density should be sufficient to determine about how many marshmallows fit in a typical measuring cup.
Conclusion
By looking at the estimated size of regular marshmallows and the interior volumes of standard measuring cups, we calculated approximate ranges for how many marshmallows can be packed into the cups:
- 8 ounce cup holds about 48 marshmallows
- 16 ounce cup holds about 95 marshmallows
This was based on the assumption marshmallows achieve around 50% packing density when compacted into the cups. The actual numbers may vary somewhat in practice based on specific conditions, but our estimates provide reasonable ballpark figures for expectation when filling measuring cups with regular marshmallows.
