Grain Bin Calculator: Capacity, Bushels & Weight
Use this grain bin calculator to turn bin dimensions into clear answers fast. Enter your sidewall height, roof rise, and either radius or diameter for round bins. Switch to rectangular to work with length and width. The tool outputs total volume, grain volume in US bushels, and total grain weight based on your chosen bulk density. You also get options for curved or conical roofs and a hopper subtraction so your numbers reflect real storage conditions.
How to use the Grain Bin Calculator
You can get accurate results in under a minute. Follow these steps.
- Choose Round or Rectangular under “Grain bin type.”
- Pick a roof style: No, Conical, or Curved.
- Enter dimensions. Round uses radius or diameter plus sidewall height. Rectangular uses length, width, and sidewall height.
- If the roof is conical or curved then add the roof height / rise.
- Check the hopper box if your bin has one. Enter hopper height to subtract it from capacity.
- Set your preferred units for each field. Switch output units anytime.
- Type a grain density if you want weight. The calculator multiplies volume by density.
The results panel shows three outputs side by side. Volume, grain volume in US bushels, and total grain weight. You can change the volume and mass units without retyping any inputs.
What this calculator measures
- Total volume of the bin interior in cubic meters, cubic feet, or US gallons.
- Grain volume in bushels using the US bushel standard. This is common in grain contracts and merchandizing.
- Total grain weight using your selected bulk density. Results display in kilograms or pounds.
The tool models real geometry rather than rough rules of thumb. Round bins use a cylinder plus a cone or spherical cap. Rectangular bins use a rectangular prism plus a pyramid or a barrel-vault roof. A hopper subtracts as a cone or a rectangular pyramid. That approach keeps your math transparent and repeatable.
Formulas for round bins
Round grain bins come in two common roof styles. A conical roof or a curved roof. The calculator handles both with standard geometry.
Cylinder (sidewall)
- Radius \( r \)
- Sidewall height \( h_s \)
- Volume: \( V_\text{cyl} = \pi r^2 h_s \)
Conical roof
- Roof rise \( h_r \)
- Volume: \( V_\text{cone} = \frac{\pi r^2 h_r}{3} \)
Curved roof (spherical cap)
- Cap height \( h_r \) over the same base radius \( r \)
- Sphere radius \( R = \frac{h_r^2 + r^2}{2h_r} \)
- Volume: \( V_\text{cap} = \frac{\pi h_r^2 (3R – h_r)}{3} \)
Hopper subtraction (round)
- Hopper height \( h_h \)
- Subtracted volume: \( V_\text{hopper} = \frac{\pi r^2 h_h}{3} \)
Total round bin volume equals the cylinder plus the roof minus the hopper. Choose the roof model that fits your bin. A curved roof holds slightly more grain than a conical roof with the same rise because a spherical cap bulges above the cone line.
Useful references: the cylinder, cone, and spherical cap geometry pages provide background and proofs.
Formulas for rectangular bins
Many on-farm storages and flat-bottom sheds are rectangular. The calculator supports flat roofs, conical peaks, and curved barrel-vault roofs.
Rectangular prism (sidewall)
- Length \( L \), width \( W \), sidewall height \( h_s \)
- Volume: \( V_\text{prism} = L \times W \times h_s \)
Conical roof analog (rectangular pyramid)
- Roof rise \( h_r \)
- Volume: \( V_\text{pyr} = \frac{L \times W \times h_r}{3} \)
Curved roof analog (barrel-vault / cylindrical segment)
- Span the curve across the width \( W \) then extrude it along \( L \).
- Rise \( h_r \) creates a circular arc segment with radius \( R = \frac{h_r^2 + (W/2)^2}{2h_r} \).
- Segment area:
\( A_\text{seg} = R^2 \cos^{-1}\!\Big(\frac{R-h_r}{R}\Big) – (R – h_r)\sqrt{2Rh_r – h_r^2} \). - Roof volume: \( V_\text{vault} = A_\text{seg} \times L \).
Hopper subtraction (rectangular)
- Subtract a rectangular pyramid under the floor or a central trough if present.
- Volume: \( V_\text{hop,rect} = \frac{L \times W \times h_h}{3} \).
This curved-roof method matches a simple barrel vault. Engineers use it in arch and shed design. See the circular segment entry for the area formula.
Simple geometry diagram
Units, conversions, and US bushels
The calculator supports metric and imperial units. You can mix inputs. It converts to SI internally then returns outputs in the units you select.
US bushels
One US bushel equals 2,150.42 cubic inches or 35.23907 liters. That’s the NIST definition used by US commerce. We convert m³ to bushels with:
\( \text{bushels} = \frac{\text{m}^3}{0.03523907} \).
Common length conversions
| Convert | To meters |
|---|---|
| 1 foot (ft) | 0.3048 m |
| 1 inch (in) | 0.0254 m |
| 1 yard (yd) | 0.9144 m |
Common volume conversions
| Convert | To cubic meters |
|---|---|
| 1 cubic foot (ft³) | 0.0283168466 m³ |
| 1 US gallon | 0.003785411784 m³ |
| 1 US bushel | 0.03523907 m³ |
If you publish capacity in both systems then keep a single source of truth. Convert everything from SI to avoid rounding drift across documents.
Grain density & test weight guide
Weight depends on volume and bulk density. Density changes with moisture, variety, and test weight. The table below lists typical values you can use as a starting point.
| Commodity | Common test weight (lb/bu) | Approx. bulk density (kg/m³) | Notes & sources |
|---|---|---|---|
| Corn (shelled) | 56 lb/bu | ~720 kg/m³ | USDA grade specs list 56 lb/bu for No. 2 corn. See USDA AMS Grain Standards. |
| Wheat | 60 lb/bu | ~770–790 kg/m³ | Varies by class and moisture. See USDA wheat standards. |
| Soybeans | 60 lb/bu | ~760–780 kg/m³ | Check local merchandiser schedules. Regional averages differ. |
| Barley | 48 lb/bu | ~600–650 kg/m³ | Malted barley numbers run lower at higher moisture. |
Treat these as ballpark figures. For contracts that settle on test weight you should enter the density that matches your measured moisture and grade. If you need a quick conversion from test weight to kg/m³ then Approx. kg/m³ ≈ (lb/bu) × 12.87 gives a useful estimate because one US bushel occupies 0.03523907 m³.
Common scenarios and pro tips
1) Fill to the eave vs include the roof
Some operations only fill to the eave. Others fill the roof. The calculator can produce both numbers. Set the roof to “No” for eave-only capacity. Choose your actual roof style to include that extra volume. This decision alone can swing totals by several percent.
2) Curved vs conical roof
A curved roof (spherical cap on round bins, barrel-vault on rectangular sheds) stores more grain for the same rise. If you switch your roof style in the tool you will see the difference. You can use that spread as a quick sensitivity check when planning a retrofit.
3) Hopper subtraction
Hoppers simplify unloading but they steal capacity. The checkbox subtracts a cone or a rectangular pyramid from the total. If your hopper measures along the outside then subtract sheet thickness first for best accuracy.
4) Moisture and weight
Weight changes with moisture content. If you track fan run time and ambient humidity you can tighten your density input over the season. Many producers keep a small note in the scale shack with typical values. It pays off during busy weeks.
5) Unit sanity checks
- If you switch to inches then check the magnitude. Numbers get big fast.
- Bushels rise with volume. If bushels fall after you increase dimensions then a unit is off.
- Weights should scale linearly with density. Double the density then weight doubles.
Worked example
Let’s run a rectangular shed with a curved roof since that setup often causes confusion.
- Length \( L = 9\,\text{m} \)
- Width \( W = 5\,\text{m} \)
- Sidewall height \( h_s = 9\,\text{m} \)
- Curved roof rise \( h_r = 2\,\text{m} \)
- No hopper
- Density \( \rho = 720\,\text{kg/m}^3 \) (shelled corn)
Body volume: \( V_\text{prism} = L \times W \times h_s = 9 \times 5 \times 9 = 405 \,\text{m}^3 \).
Roof radius: \( R = \frac{h_r^2 + (W/2)^2}{2h_r} = \frac{4 + 2.5^2}{4} = 2.5625 \,\text{m} \).
Segment area:
\( A_\text{seg} = R^2 \cos^{-1}(\tfrac{R-h_r}{R}) – (R-h_r)\sqrt{2Rh_r – h_r^2} \approx 7.4549 \,\text{m}^2 \).
Vault volume: \( V_\text{vault} = A_\text{seg} \times L \approx 7.4549 \times 9 = 67.095 \,\text{m}^3 \).
Total volume: \( V \approx 472.095 \,\text{m}^3 \).
Bushels: \( V / 0.03523907 \approx 13{,}396.9 \,\text{US bu} \).
Weight: \( V \times \rho \approx 472.095 \times 720 = 339{,}908\,\text{kg} \). Convert to pounds if needed by multiplying by 2.20462.
Every step follows published geometry and the NIST bushel standard. Numbers scale in a predictable way when you change a dimension which makes planning easier.
Frequently asked questions
Why do my results differ from another online calculator?
Two reasons top the list. Some tools ignore the roof volume when they show “capacity” which reduces totals. Others use a different bushel constant. This calculator uses the NIST US bushel. You can match another tool by turning off the roof or by using their conversion factor if it is documented.
Which roof model should I pick?
If your roof has straight lines from the eave to the peak then pick Conical. If the sheets form an arc then pick Curved. Rectangular sheds with a rounded top use the curved model.
Is the radius required for rectangular bins?
No. Rectangular storage uses length, width, and sidewall height. A curved roof rides on a circular vault across the width. The calculator finds the vault radius from the width and your roof rise.
What’s the best density to use for weight?
Use the density that matches your moisture and grade. The table in this article lists handy values for planning. Your elevator ticket and test weight often provide better site-specific numbers.
Can I treat this as engineering advice?
No. It’s a planning tool. Use it to estimate capacity, compare designs, and talk with your builder or engineer. For structural loads and safety factors consult a qualified professional.
Accessibility and usability details
Every input has a label. Controls follow the tab order and work with the keyboard. Segmented toggles use real buttons. Unit selectors are native HTML selects so phones present familiar pickers. Numbers display with your locale so thousands separators match what you expect.
Troubleshooting quick answers
- If you can’t see the roof inputs then the roof is set to “No.” Pick Conical or Curved to show the rise field.
- If the bushels look low then confirm the bushel standard and that the roof is included.
- If weight doesn’t change when you edit density then the density field might be empty or set to zero. Enter a positive number.
Why this approach produces trustworthy numbers
Capacity calculations fail when they rely on oversimplified shapes. This calculator keeps each shape honest. Cylinders for round walls. Rectangular prisms for sheds. Cones or spherical caps for round roofs. Pyramids or cylindrical segments for rectangular roofs. Those shapes are textbook geometry. You can check any result with a calculator and a few lines of scratch work.
Key takeaways
- Use the roof model that matches your bin because roof volume matters.
- Pick the NIST US bushel standard for contracts that settle in US bushels.
- Enter a realistic density to turn volume into weight with confidence.
- Save a baseline set of numbers for each bin so you can compare seasons.
References and further reading
- NIST: SI units and US customary conversions
- NIST Office of Weights and Measures — US bushel definition and guidance
- USDA AMS: Official U.S. Standards for Grain — test weight references
- Spherical cap volume derivation
- Circular segment (barrel-vault) area
Ready to run your numbers? Open the calculator above, choose your bin type, and enter a few dimensions. You will see capacity and bushels update as you type. If you need help interpreting a result reach out to your builder or merchandiser with the numbers in hand.
