Funnel Volume Calculator
A physical funnel holds liquid in a sloped section that ends where the stem begins, and that shape decides which formula is honest. This calculator covers both: the Cone tab prices the classic pointed cone from top radius and height, and the new Frustum tab prices the cut-off shape a real funnel actually has, from top radius, bottom radius and height. Both return the volume in your input unit plus liters, US gallons, Imperial gallons and US cups, the weight a full funnel holds, and the slant height and lateral surface area.
The cone model treats the funnel as tapering to a point at the bottom of the height you enter. For a real funnel cut off at the stem, use the Frustum tab.
Pre-filled with the frustum worked example from the article: a lab funnel with top radius 5 cm, bottom radius 1.5 cm and sloped height 10 cm.
Quick Answer
A pointed cone holds (1/3) × π × r² × h: the pre-filled kitchen funnel, radius 3 in and height 6 in, holds 56.55 cubic inches (0.927 L, 3.92 US cups). A real funnel is a frustum, (1/3) × π × h × (R² + Rr + r²): the same top and height with a 0.5 in bottom radius holds 67.54 cubic inches, because its wall stays further out over the lower section. Which is right depends on which height you measured.
Key takeaways
- Real funnels are frustums: the sloped wall is cut off at the stem, never reaching a point.
- The cone is the frustum with bottom radius 0: set r to 0 on the Frustum tab and the two tabs agree exactly.
- Same top radius and same measured height: the frustum holds more, 19.4% more in the comparison below, because its wall sits further out.
- If your height runs to where the point would be, below the stem, the cone overstates instead. The measurement decides the direction.
- Quick Answer
- How to use the funnel volume calculator
- Cone or frustum: two shapes, two measurement situations
- Worked example: the standard 6 inch kitchen funnel
- Frustum worked example: a bench lab funnel in centimeters
- The whole funnel: stem, collar and capacity versus throughput
- What competing calculators miss
- Limits of this calculator
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the funnel volume calculator
Pick the tab that matches the funnel in front of you, measure in one unit throughout, and click Calculate.
- Choose the shape. Cone (pointed) needs two lengths. Frustum (real funnel) needs three, and it is the physically exact model for any funnel with a measurable bottom opening.
- Measure the top radius: measure straight across the opening to get the diameter, then halve it. A 6 inch wide kitchen funnel has a radius of 3 inches.
- On the Frustum tab, measure the bottom radius the same way, across the opening where the sloped wall meets the stem. On a typical kitchen funnel that opening is about an inch across, radius near 0.5 in.
- Measure the vertical height of the sloped section, rim to stem joint, straight down. Do not run the tape along the sloped side and do not include the stem: that slope is the slant height, which the tool derives, and the stem is a separate cylinder.
- Choose inches, centimeters or millimeters and set the liquid weight if you need it. The field is pre-filled with 8.34 lb per US gallon for water; diesel is about 7.1 and most cooking oils sit near 7.7. Clear the field, or enter zero, and the weight line reports not computed.
Two traps account for nearly every wrong funnel figure. The first is entering the diameter where the radius belongs, which quadruples a cone result because the radius is squared. The second is folding extra parts into the height: a top collar and the stem are cylinders, not cone or frustum, and the real-funnel section below prices them with a cylinder capacity calculator instead.
Cone or frustum: two shapes, two measurement situations
A frustum is what remains when a cone’s tip is cut off parallel to the base. Keep both radii and the height of what is left, and the volume is fixed.
Cone (pointed)
V = (1/3) π R² h. The wall narrows to a point at the bottom of h.
Frustum (cut off)
V = (1/3) π h (R² + Rr + r²). The wall stops at radius r, where the stem begins.
The two tabs answer different measurement situations. If you measured the sloped section itself, rim to stem joint, the frustum is exact for that section and the cone with the same top radius and height runs low, because the cone model keeps narrowing to a point inside your measured height. If instead you estimated the height by extending the wall lines down to the point they would meet, below the physical funnel, the cone counts a small cone that does not exist under the stem, and it runs high. The older version of this page warned only about the second case. Both are real; the tape measure decides which one you are in.
The frustum formula is standard geometry: the Wolfram MathWorld entry on the conical frustum gives the volume as (1/3) π h (R² + Rr + r²), the slant height as the square root of h² plus (R − r)², and the lateral area as π (R + r) times the slant height, exactly the three quantities the Frustum tab computes. The cone is the limiting case: set r to 0 and the frustum formula collapses to (1/3) π R² h, the formula in the MathWorld entry on the cone. Textbooks reach the same result by slicing the solid into thin discs and summing them, the method worked through in OpenStax Calculus, section 6.2 on determining volumes by slicing and the matching LibreTexts Calculus chapter. Conversions run through cubic centimeters using the exact inch of 2.54 cm and the unit relationships in the NIST Guide for the Use of the International System of Units (SP 811): a liter is 1,000 cm³, a US gallon is 3,785.411784 cm³, an Imperial gallon is 4,546.09 cm³ and a US cup is 236.5882365 cm³, consistent with the BIPM SI Brochure.
Worked example: the standard 6 inch kitchen funnel
The Cone tab is pre-filled with a common kitchen funnel: radius 3 inches, height 6 inches, filled with water. Running the formula by hand gives the same outputs the calculator shows.
- V = (1/3) × π × 3² × 6 = 56.55 cubic inches
- Liters: 56.55 in³ = 926.7 cm³ = 0.927 L; US cups: 3.92
- Slant s = √(9 + 36) = 6.71 in
- Lateral area = π × 3 × 6.7082 = 63.22 sq in
- Weight of a full funnel of water: 0.245 US gal × 8.34 = 2.04 lb
Now measure the same funnel honestly. Its sloped wall ends at a stem opening about an inch across, a bottom radius of 0.5 in, and the sloped height is still 6 in. The Frustum tab gives V = (1/3) π × 6 × (9 + 1.5 + 0.25) = 67.54 cubic inches (1.107 L, 4.68 cups), slant height √(36 + 6.25) = 6.50 in exactly, lateral area π × 3.5 × 6.5 = 71.47 sq in. The frustum holds 10.99 cubic inches more, 19.4% more, because over the lower half its wall sits up to half an inch further out than the cone’s wall at the same depth. Neither number is a mistake: two different solids share a rim and a height.
| Model, same funnel (R 3 in, h 6 in) | Volume | Liters | US cups | Slant | Lateral area |
|---|---|---|---|---|---|
| Cone, pointed (r = 0) | 56.55 in³ | 0.927 | 3.92 | 6.71 in | 63.22 sq in |
| Frustum, bottom radius 0.5 in | 67.54 in³ | 1.107 | 4.68 | 6.50 in | 71.47 sq in |
| Difference | +10.99 in³ | +0.180 | +0.76 | −0.21 in | +8.25 sq in |
Frustum worked example: a bench lab funnel in centimeters
The Frustum tab is pre-filled with a bench funnel measured in centimeters: top radius 5 cm, bottom radius 1.5 cm, sloped height 10 cm. Worked by hand:
- R² + Rr + r² = 25 + 7.5 + 2.25 = 34.75
- V = (1/3) × π × 10 × 34.75 = 363.90 cm³ = 0.364 L (1.54 US cups)
- Slant s = √(10² + (5 − 1.5)²) = √112.25 = 10.59 cm
- Lateral area = π × (5 + 1.5) × 10.5948 = 216.35 sq cm
Lab funnels are where the frustum earns its keep. A powder or filtration funnel is short and wide with a broad stem opening, so the bottom radius is a large share of the top radius and the cone shortcut drifts furthest from the truth. Nominal lab capacities are quoted to the rim, while a funnel in use is filled below the rim, so treat the computed figure as the geometric capacity of the sloped section and leave working headroom. For vessels that are not funnels at all, odd shapes are the territory of the container volume calculator, and if the job is the volume needed to fill a space rather than a vessel’s capacity, the fill volume calculator covers that side.
The whole funnel: stem, collar and capacity versus throughput
The sloped section is most of a funnel, but not all of it, and capacity is not the only number that matters.
The stem. Below the frustum sits a straight tube. Its volume is π × stem radius² × stem length: a stem of radius 0.25 in and length 2 in adds 0.39 cubic inches, under 1% of the comparison funnel’s frustum capacity. Add it for long, wide stems and skip it for standard kitchen funnels. Sizing a round receiving vessel is the ball volume calculator’s job.
The collar. Some funnels carry a short straight band at the top. Price it as a cylinder of the top radius and add it; folding it into the sloped height understates the total, because a cylinder holds three times its cone equivalent.
Capacity versus throughput. Both tabs answer how much the funnel holds at one instant, not how fast it drains. Drain speed is set by the stem’s narrowest opening, the liquid’s thickness and the air path back into the receiving vessel, none of which a volume formula can see. A wide frustum on a narrow stem holds a lot and still pours slowly: batch volume and funnel capacity are different questions.
What competing calculators miss
Funnel tools split into camps:
- The composite-shape tool (CalculatorsHub, the top result for this search): models a funnel as a cylindrical top section plus a conical frustum and asks for a bottom radius, the right physical instinct. But it works in centimeters only, splits the shape across two section heights, and offers no cups, gallons or liquid weight.
- Cone-only funnel tools (BraveCalculator, CalculatorUltra, and this page before the rebuild): top radius and height into (1/3)πr²h, full stop. Fine for a pointed solid, silent about the stem cut-off every real funnel has.
- General cone calculators: correct cone math, sometimes with total surface area a funnel does not need, but nothing funnel-specific: no bottom radius, no liquid weight, no diameter-trap warning.
- The gap this page now fills: both shapes on one page, the cone kept intact as the bottom-radius-0 case, three input units, six volume restatements including both gallon standards, a liquid weight line driven by a density figure you control, and an honest account of when each model runs high or low.
Limits of this calculator
Both models assume a right circular shape: a round rim, straight sloped walls and a vertical axis. Curved (trumpet) walls, an oval rim or a ribbed interior will differ from both formulas, and the frustum figure covers the sloped section only, never the stem or a top collar. Wall thickness matters at small sizes: enter inside measurements for capacity, because outside measurements on a thick-walled lab funnel overstate what it holds. The weight line is only as good as the pounds-per-gallon figure you supply, and it describes a funnel filled level to the rim, a measuring convention, not a pouring recommendation.
Frequently asked questions
For a pointed funnel the volume is (1/3) × π × r² × h, where r is the top radius and h is the vertical height. For a real funnel cut off at the stem, use the frustum formula on the Frustum tab: (1/3) × π × h × (R² + Rr + r²), where R is the top radius and r is the bottom radius. The one-third is what separates a cone from a cylinder of the same base and height.
Enter the radius, which is half the diameter. Measure straight across the opening, then halve the number before typing it in. Entering the diameter by mistake quadruples the cone result, because the radius is squared.
Use the Frustum tab when you can measure the opening where the sloped wall meets the stem: that is the shape a real funnel has. Use the Cone tab when the stem opening is tiny compared with the top, or when you only have the top radius and height: the cone is then a close approximation, and setting the bottom radius to 0 on the Frustum tab gives the identical number.
Because the walls are in different places. The cone keeps narrowing all the way to a point at the bottom of the measured height, while the frustum stops narrowing at the bottom radius and its wall sits further out over the lower part. A frustum with top radius 3 in, bottom radius 0.5 in and height 6 in holds 67.54 cubic inches against the cone’s 56.55. If instead you measured the height all the way to where the point would be, below the stem, the cone figure overstates the frustum section, which is the case the older version of this page warned about.
No. Both tabs price the sloped section only. The stem is a tube, so add it separately as a cylinder: π × stem radius² × stem length. A stem of radius 0.25 in and length 2 in adds 0.39 cubic inches, under 1% of the worked example’s frustum capacity, so it only matters for long or wide stems.
Read the US cups line in the results: it is the volume divided by 236.5882365 cubic centimeters per cup. The worked-example cone holds 3.92 cups, and the same top and height measured as a frustum with a 0.5 in bottom radius holds 4.68 cups.
The tool rejects it, because a funnel narrows downward. A bottom radius larger than the top radius usually means the two measurements were swapped, or the shape is a flared vessel rather than a funnel, which neither formula describes.
The weight line shows not computed when the liquid weight field is blank or zero. Enter a positive pounds-per-US-gallon figure, 8.34 for water, and the tool multiplies it by the US gallon volume to give the weight of a full funnel. Diesel is about 7.1 and most cooking oils sit near 7.7.
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References
- Wolfram Research. Conical Frustum, Wolfram MathWorld. Accessed October 21, 2026.
- Wolfram Research. Cone, Wolfram MathWorld. Accessed October 21, 2026.
- OpenStax, Rice University. Determining Volumes by Slicing, Calculus Volume 1, Section 6.2. Accessed October 21, 2026.
- LibreTexts. Determining Volumes by Slicing, Calculus (OpenStax), Section 6.02. Accessed October 21, 2026.
- National Institute of Standards and Technology. Guide for the Use of the International System of Units (SI), Special Publication 811. Accessed October 21, 2026.
- Bureau International des Poids et Mesures (BIPM). The International System of Units (SI Brochure). Accessed October 21, 2026.