Volume Calculator
Calculate the volume of 3D shapes including cubes, rectangular prisms, cylinders, spheres, cones, pyramids, and ellipsoids. Convert between cubic feet, cubic meters, gallons, liters, and cubic yards.
Rectangular Prism Diagram
V = l × w × hEnter Dimensions
Volume
320.0 cu ft
Volume Quick Reference
- 1 cu yd = 27 cu ft
- 1 cu ft = 7.48 gallons
- 1 cu m = 35.31 cu ft
- 1 cu m = 264.17 gallons
- 5-gallon bucket: 0.67 cu ft
- Bathtub: 40-60 gallons
- Hot tub: 300-500 gallons
- Concrete truck: 8-10 cu yd
- For cylinders and spheres, always use radius (half the diameter), not the full diameter
- Cones and pyramids hold exactly 1/3 the volume of cylinders/prisms with the same base and height
- Add 5-10% extra when ordering bulk materials to account for waste and settling
- 1 cubic yard of concrete weighs about 4,000 lbs (2 tons)
- For horizontal tanks, half-full depth does NOT equal half volume due to curved shape
Related Calculators
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About This Calculator
Calculate the volume of any 3D shape instantly with this comprehensive volume calculator. Whether you need to determine how much material fits in a container, calculate concrete for a project, or solve geometry problems, this tool handles cubes, rectangular prisms, cylinders, spheres, cones, pyramids, and ellipsoids with precision.
Why accurate volume calculation matters: From construction projects to shipping logistics, knowing exact volumes prevents costly errors. Underestimating concrete by just 0.5 cubic yards on a patio pour means stopping mid-project and creating weak cold joints. Overestimating fill material by 20% on a landscaping project could waste $200-$500 in unnecessary materials.
Common volume calculation scenarios:
- Construction: Concrete pours, fill dirt, gravel, excavation
- Landscaping: Mulch, topsoil, compost, decorative stone
- Shipping: Package dimensions, container capacity, freight volume
- Storage: Tank capacity, bin volume, warehouse space
- Science: Lab measurements, chemical volumes, liquid capacity
- Cooking: Recipe scaling, container sizing, bulk ingredients
This calculator provides instant results in multiple units (cubic feet, cubic meters, gallons, liters, cubic yards) and includes visual diagrams showing exactly which dimensions to measure. Enter your measurements and get accurate results for any 3D volume calculation.
How to Use the Volume Calculator
- 1Select the 3D shape you want to calculate from the shape selector (cube, rectangular prism, cylinder, sphere, cone, pyramid, or ellipsoid).
- 2Enter the required dimensions for your selected shape. The input fields automatically adjust to show only what's needed for each shape.
- 3View the interactive SVG diagram showing your shape with labeled dimensions for visual confirmation.
- 4Read the calculated volume displayed in your primary unit (cubic feet by default).
- 5Use the unit converter dropdown to see your volume in cubic meters, gallons, liters, or cubic yards.
- 6Review the complete unit conversion table showing your volume in all available units simultaneously.
- 7Copy, share, or print your results using the action buttons below the calculation.
Formula
Cube: V = s^3 | Prism: V = lwh | Cylinder: V = pi*r^2*h | Sphere: V = (4/3)*pi*r^3Each 3D shape has a unique volume formula based on its geometry. Cube volume is side cubed. Rectangular prism volume is length times width times height. Cylinder volume uses pi times radius squared times height. Sphere volume is four-thirds pi times radius cubed. Cone volume is one-third the cylinder formula. All formulas work with any consistent unit system, just ensure all inputs use the same unit.
Volume Formulas for All Common 3D Shapes
Master these essential volume formulas for accurate calculations:
Cube and Rectangular Prism:
| Shape | Formula | Example |
|---|---|---|
| Cube | V = s^3 | 4 ft side: 4^3 = 64 cu ft |
| Rectangular Prism | V = l x w x h | 5 x 4 x 3 ft = 60 cu ft |
The rectangular prism (box) formula is the most commonly used. It applies to rooms, shipping containers, pools, and most storage spaces.
Cylinder:
| Measurement | Formula | Example |
|---|---|---|
| Volume | V = pi x r^2 x h | r=3 ft, h=5 ft: pi x 9 x 5 = 141.37 cu ft |
| Using diameter | V = pi x (d/2)^2 x h | d=6 ft, h=5 ft: pi x 9 x 5 = 141.37 cu ft |
Critical: Always use radius (half the diameter), not the full diameter. Using diameter directly gives 4x the correct answer.
Sphere:
| Shape | Formula | Example |
|---|---|---|
| Full sphere | V = (4/3) x pi x r^3 | r=2 ft: (4/3) x pi x 8 = 33.51 cu ft |
| Hemisphere | V = (2/3) x pi x r^3 | Half of sphere formula |
Sphere volume grows cubically with radius. Doubling radius increases volume 8x.
Cone:
| Shape | Formula | Example |
|---|---|---|
| Cone | V = (1/3) x pi x r^2 x h | r=3 ft, h=6 ft: (1/3) x pi x 9 x 6 = 56.55 cu ft |
A cone holds exactly 1/3 the volume of a cylinder with the same base and height.
Pyramid:
| Base Shape | Formula | Example |
|---|---|---|
| Square base | V = (1/3) x s^2 x h | s=4 ft, h=6 ft: (1/3) x 16 x 6 = 32 cu ft |
| Rectangular base | V = (1/3) x l x w x h | 4 x 3 x 6 ft: (1/3) x 72 = 24 cu ft |
Like cones, pyramids hold 1/3 the volume of a prism with the same base and height.
Ellipsoid:
| Shape | Formula | Example |
|---|---|---|
| Ellipsoid | V = (4/3) x pi x a x b x c | a=3, b=2, c=4: (4/3) x pi x 24 = 100.53 cu ft |
Where a, b, and c are the three semi-axes (half the full dimensions in each direction).
Volume Unit Conversions
Convert between volume units with these precise conversion factors:
Cubic Units:
| From | To | Multiply by |
|---|---|---|
| Cubic feet (cu ft) | Cubic inches (cu in) | 1,728 |
| Cubic feet | Cubic yards (cu yd) | 0.037037 (or / 27) |
| Cubic feet | Cubic meters (m^3) | 0.0283168 |
| Cubic yards | Cubic feet | 27 |
| Cubic yards | Cubic meters | 0.764555 |
| Cubic meters | Cubic feet | 35.3147 |
| Cubic meters | Cubic yards | 1.30795 |
Liquid Units (US):
| From | To | Multiply by |
|---|---|---|
| Cubic feet | US Gallons | 7.48052 |
| Cubic feet | US Quarts | 29.9221 |
| Cubic feet | Liters | 28.3168 |
| Cubic yards | US Gallons | 201.974 |
| US Gallons | Cubic feet | 0.133681 |
| US Gallons | Liters | 3.78541 |
| Liters | US Gallons | 0.264172 |
| Liters | Cubic feet | 0.0353147 |
Quick Reference Conversions:
| Volume | Cubic Feet | Cubic Yards | Gallons | Liters |
|---|---|---|---|---|
| 1 cu ft | 1 | 0.037 | 7.48 | 28.32 |
| 1 cu yd | 27 | 1 | 201.97 | 764.55 |
| 1 cu m | 35.31 | 1.31 | 264.17 | 1,000 |
| 100 gal | 13.37 | 0.495 | 100 | 378.54 |
| 1,000 L | 35.31 | 1.31 | 264.17 | 1,000 |
Weight Estimates (varies by material density):
| Material | Weight per Cu Ft | Weight per Cu Yd |
|---|---|---|
| Water | 62.4 lbs | 1,685 lbs |
| Concrete | 150 lbs | 4,050 lbs |
| Gravel | 100-120 lbs | 2,700-3,240 lbs |
| Mulch | 15-30 lbs | 400-800 lbs |
| Topsoil | 75-100 lbs | 2,000-2,700 lbs |
| Sand (dry) | 100 lbs | 2,700 lbs |
Real-World Volume Applications
Apply volume calculations to common projects:
Construction Materials:
| Material | Typical Unit | Coverage | 2026 Price Range |
|---|---|---|---|
| Concrete | Cubic yard | Slabs, footings, foundations | $140-$200/cu yd delivered |
| Fill dirt | Cubic yard | Grading, fill | $20-$50/cu yd |
| Gravel | Cubic yard | Driveways, drainage | $35-$75/cu yd |
| Sand | Cubic yard | Leveling, masonry | $40-$60/cu yd |
| Crushed stone | Cubic yard | Base material | $45-$85/cu yd |
Landscaping Materials:
| Material | Depth | Coverage per Cu Yd | Price Range |
|---|---|---|---|
| Mulch | 2" | 162 sq ft | $30-$60/cu yd |
| Mulch | 3" | 108 sq ft | $30-$60/cu yd |
| Mulch | 4" | 81 sq ft | $30-$60/cu yd |
| Topsoil | 2" | 162 sq ft | $35-$65/cu yd |
| Compost | 2" | 162 sq ft | $40-$80/cu yd |
| Decorative rock | 2" | 100-120 sq ft | $100-$300/cu yd |
Tank and Container Capacities:
| Container Type | Common Sizes | Cubic Feet | Gallons |
|---|---|---|---|
| 55-gallon drum | 23" dia x 35" | 7.35 | 55 |
| 275-gallon IBC tote | 48" x 40" x 46" | 36.74 | 275 |
| Pickup truck bed (level) | 8 ft bed | 45-80 cu ft | 2-3 cu yd |
| Standard dumpster | 20 cu yd | 540 cu ft | 4,039 gal |
| Swimming pool (avg) | 15 x 30 x 5 ft | 2,250 cu ft | 16,830 gal |
Shipping and Freight:
| Container | Interior Dimensions | Cubic Feet | Cubic Meters |
|---|---|---|---|
| 20' container | 19'4" x 7'9" x 7'10" | 1,172 | 33.2 |
| 40' container | 39'5" x 7'8" x 7'10" | 2,390 | 67.7 |
| 40' HC container | 39'5" x 7'8" x 8'10" | 2,700 | 76.5 |
| 53' trailer | 53' x 8'6" x 9' | 4,050 | 114.7 |
Related CalculatorJar Calculators:
- Concrete Calculator: Calculate cubic yards for slabs, footings, and columns with cost estimates
- Mulch Calculator: Determine mulch volume needed based on area and depth
- Gravel Calculator: Calculate gravel, sand, and stone quantities for landscaping
- Area Calculator: Calculate 2D areas for floors, walls, and land
- Cylinder Volume Calculator: Specialized calculations for cylindrical tanks and pipes
Cylinder Volume Deep Dive
Cylinders are among the most common 3D shapes in real-world applications:
Basic Cylinder Formula:
- V = pi x r^2 x h
- Where r = radius (half the diameter)
- And h = height (or length for horizontal cylinders)
Common Cylinder Calculations:
| Diameter | Radius | Height | Volume (cu ft) | Gallons |
|---|---|---|---|---|
| 2 ft | 1 ft | 4 ft | 12.57 | 94 |
| 3 ft | 1.5 ft | 4 ft | 28.27 | 212 |
| 4 ft | 2 ft | 4 ft | 50.27 | 376 |
| 6 ft | 3 ft | 4 ft | 113.10 | 846 |
| 8 ft | 4 ft | 4 ft | 201.06 | 1,504 |
| 10 ft | 5 ft | 4 ft | 314.16 | 2,350 |
Horizontal vs. Vertical Cylinders:
For upright cylinders, calculating full volume is straightforward. For horizontal cylinders (like propane tanks or buried storage tanks), partial fill calculations are more complex:
- Segment formula: V = L x [r^2 x arccos((r-h)/r) - (r-h) x sqrt(2rh-h^2)]
- Where L = length, r = radius, h = liquid depth
Tank Fill Levels:
| Fill Level | Percentage of Full Volume |
|---|---|
| 1/4 full (horizontal) | ~20% (not 25%!) |
| 1/2 full | 50% |
| 3/4 full (horizontal) | ~80% (not 75%!) |
This asymmetry occurs because cylinders are wider in the middle than at the top/bottom.
Pipe Volume (per linear foot):
| Pipe Diameter | Volume per Foot | Gallons per Foot |
|---|---|---|
| 2" | 0.0218 cu ft | 0.163 gal |
| 3" | 0.0491 cu ft | 0.367 gal |
| 4" | 0.0873 cu ft | 0.653 gal |
| 6" | 0.196 cu ft | 1.47 gal |
| 8" | 0.349 cu ft | 2.61 gal |
| 12" | 0.785 cu ft | 5.87 gal |
Cylinder vs. Rectangular Tank Comparison:
For the same volume, cylinders use about 13% less material (surface area) than rectangular tanks. This explains why most large storage tanks are cylindrical - material efficiency at scale.
Sphere and Cone Volume Calculations
Master curved shape volume calculations:
Sphere Volume Formula:
- V = (4/3) x pi x r^3
- Or using diameter: V = (pi/6) x d^3
Sphere Volume Quick Reference:
| Diameter | Radius | Volume (cu ft) | Volume (gallons) |
|---|---|---|---|
| 1 ft | 0.5 ft | 0.52 | 3.9 |
| 2 ft | 1 ft | 4.19 | 31.3 |
| 3 ft | 1.5 ft | 14.14 | 105.8 |
| 4 ft | 2 ft | 33.51 | 250.7 |
| 6 ft | 3 ft | 113.10 | 846.2 |
| 8 ft | 4 ft | 268.08 | 2,005.4 |
| 10 ft | 5 ft | 523.60 | 3,916.5 |
Hemisphere (Half Sphere):
- V = (2/3) x pi x r^3
- Exactly half the full sphere volume
Cone Volume Formula:
- V = (1/3) x pi x r^2 x h
- A cone holds exactly 1/3 of a cylinder with the same base and height
Cone Volume Quick Reference:
| Base Diameter | Height | Volume (cu ft) | Volume (gallons) |
|---|---|---|---|
| 2 ft | 3 ft | 3.14 | 23.5 |
| 3 ft | 4 ft | 9.42 | 70.5 |
| 4 ft | 5 ft | 20.94 | 156.7 |
| 6 ft | 8 ft | 75.40 | 564.1 |
| 8 ft | 10 ft | 167.55 | 1,253.4 |
Truncated Cone (Frustum):
For cones with the top cut off (like many hoppers and funnels):
- V = (1/3) x pi x h x (R^2 + R x r + r^2)
- Where R = bottom radius, r = top radius, h = height
Real-World Applications:
| Shape | Common Uses |
|---|---|
| Sphere | Water towers, gas storage tanks, ball capacity |
| Hemisphere | Dome structures, bowl capacity, igloo volume |
| Cone | Funnel capacity, pile volume (gravel, sand), roof sections |
| Truncated cone | Planters, hoppers, bucket capacity, lamp shades |
The "Cone of Gravel" Problem:
When gravel, sand, or mulch is dumped, it naturally forms a cone with a consistent angle (angle of repose, typically 25-45 degrees). To estimate a pile's volume:
- Measure base diameter and height
- Apply cone formula: V = (1/3) x pi x r^2 x h
- This works for any granular material pile
Pyramid and Ellipsoid Volume Calculations
Complete your volume calculation toolkit with these shapes:
Pyramid Volume Formula:
- Square base: V = (1/3) x s^2 x h
- Rectangular base: V = (1/3) x l x w x h
- Any base: V = (1/3) x Base Area x h
Like cones, pyramids hold exactly 1/3 the volume of a prism with the same base and height.
Pyramid Volume Quick Reference (Square Base):
| Base Side | Height | Volume (cu ft) |
|---|---|---|
| 2 ft | 3 ft | 4.0 |
| 3 ft | 4 ft | 12.0 |
| 4 ft | 5 ft | 26.67 |
| 5 ft | 6 ft | 50.0 |
| 6 ft | 8 ft | 96.0 |
| 10 ft | 15 ft | 500.0 |
Truncated Pyramid (Frustum):
For pyramids with the top cut off:
- Square bases: V = (1/3) x h x (A1 + A2 + sqrt(A1 x A2))
- Where A1 = bottom area, A2 = top area, h = height
Ellipsoid Volume Formula:
- V = (4/3) x pi x a x b x c
- Where a, b, c are the three semi-axes
Ellipsoid Quick Reference:
| Semi-axes (a x b x c) | Volume (cu ft) |
|---|---|
| 1 x 1 x 1 (sphere) | 4.19 |
| 2 x 1 x 1 (prolate) | 8.38 |
| 2 x 2 x 1 (oblate) | 16.76 |
| 3 x 2 x 1 | 25.13 |
| 3 x 2 x 2 | 50.27 |
| 4 x 3 x 2 | 100.53 |
Special Ellipsoid Cases:
| Type | Description | Formula |
|---|---|---|
| Sphere | All semi-axes equal (a=b=c) | V = (4/3) x pi x r^3 |
| Prolate spheroid | Football shape (a>b=c) | V = (4/3) x pi x a x b^2 |
| Oblate spheroid | Flattened sphere (a=b>c) | V = (4/3) x pi x a^2 x c |
| Scalene ellipsoid | All different (a ne b ne c) | V = (4/3) x pi x a x b x c |
Real-World Ellipsoid Applications:
| Shape | Common Uses |
|---|---|
| Prolate spheroid | Footballs, airships, submarines |
| Oblate spheroid | Earth (slightly flattened at poles), planets |
| General ellipsoid | Egg volume, tank designs, 3D modeling |
Earth as an Ellipsoid:
The Earth is an oblate spheroid with:
- Equatorial radius: 3,963.2 miles
- Polar radius: 3,949.9 miles
- Volume: approximately 260 billion cubic miles
This slight flattening (about 0.3%) affects precise calculations for navigation, surveying, and satellite orbits.
Common Volume Calculation Mistakes
Avoid these frequent errors that lead to costly miscalculations:
Mistake 1: Using Diameter Instead of Radius
- Cylinder/sphere formulas use RADIUS, not diameter
- Radius = Diameter / 2
- Using diameter directly gives 4x the correct volume for cylinders, 8x for spheres
Example Error:
- Tank: 10 ft diameter, 8 ft tall
- Wrong: V = pi x 10^2 x 8 = 2,513 cu ft
- Correct: V = pi x 5^2 x 8 = 628 cu ft
- Error: 4x overestimate!
Mistake 2: Forgetting the 1/3 Factor for Cones/Pyramids
- Cones hold 1/3 the volume of a cylinder
- Pyramids hold 1/3 the volume of a prism
- Missing this factor gives 3x the correct volume
Mistake 3: Mixing Measurement Units
| Measurement | Wrong | Correct |
|---|---|---|
| 6 ft x 4 ft x 8 inches | 192 cu ft | 16 cu ft |
| 3 m x 2 m x 50 cm | 300 cu m | 3 cu m |
Always convert all dimensions to the same unit before multiplying.
Mistake 4: Confusing Volume and Capacity
- Volume is the space an object occupies
- Capacity is the volume a container can hold
- Wall thickness matters: A 10-gallon bucket with 1/4" walls holds less than calculated interior volume
Mistake 5: Ignoring Irregular Base Shapes
For containers with non-rectangular bases:
- Calculate base area using appropriate formula
- Then multiply by height
- Don't assume all "boxes" are rectangular
Mistake 6: Assuming Linear Fill Relationship
For horizontal cylinders and tapered containers, half-filled does NOT mean half the depth:
- Horizontal cylinder at 50% depth = 50% volume
- Horizontal cylinder at 25% depth = ~20% volume (not 25%)
Mistake 7: Not Accounting for Material Compaction
| Material | Compaction Factor |
|---|---|
| Loose topsoil | 0.8-0.9 (compacts 10-20%) |
| Gravel | 0.9-0.95 (compacts 5-10%) |
| Mulch | 0.7-0.8 (compacts 20-30%) |
| Concrete | 1.0 (no significant compaction) |
Order extra material to account for settling.
Mistake 8: Forgetting Unusable Space
| Container Type | Practical Fill % |
|---|---|
| Propane tanks | 80% (safety margin) |
| Water heaters | 100% but 20% dead volume |
| Shipping containers | 85-90% (packing efficiency) |
| Pickup truck (rounded load) | 1.5-2x level volume |
Verification Checklist:
- Did I use radius (not diameter) for round shapes?
- Did I apply the 1/3 factor for cones/pyramids?
- Are all my dimensions in the same unit?
- Did I account for wall thickness if measuring exterior dimensions?
- Did I add waste/compaction factor for bulk materials?
- Does the result seem reasonable for the size of the object?
Volume Calculator Cross-References
Explore related calculators for complete project planning:
Geometry Calculators:
-
Area Calculator: Calculate 2D surface areas for floors, walls, and land. Area x depth = volume for rectangular shapes.
-
Cylinder Volume Calculator: Specialized calculations for cylindrical tanks, pipes, and columns including partial fill calculations.
Construction & Landscaping:
-
Concrete Calculator: Calculate cubic yards for slabs, footings, columns, and walls. Includes bag counts, waste factors, and 2026 pricing.
-
Mulch Calculator: Determine mulch volume and bags needed based on garden area and desired depth. Includes coverage tables and cost estimates.
-
Gravel Calculator: Calculate gravel, crushed stone, and sand quantities for driveways, pathways, and drainage projects.
Why Cross-Reference:
| Starting With | You'll Also Need |
|---|---|
| Box volume (cu ft) | Concrete calculator for cubic yards |
| Area (sq ft) + depth | This volume calculator |
| Tank diameter/height | Gallon capacity conversion |
| Bulk material volume | Weight and delivery estimates |
| Shipping dimensions | Dimensional weight calculations |
Project Planning Workflow:
- Measure dimensions using this volume calculator
- Convert units if needed (cu ft to cu yd, gallons, etc.)
- Add waste factor based on material type (5-20%)
- Calculate materials using specialized calculators
- Estimate costs with local pricing and delivery fees
Volume-to-Weight Conversions:
For estimating delivery weights and costs:
| Material | Lbs per Cu Ft | Lbs per Cu Yd | Tons per Cu Yd |
|---|---|---|---|
| Water | 62.4 | 1,685 | 0.84 |
| Concrete | 150 | 4,050 | 2.03 |
| Gravel (loose) | 95 | 2,565 | 1.28 |
| Sand (dry) | 100 | 2,700 | 1.35 |
| Topsoil | 75 | 2,025 | 1.01 |
| Mulch (wood) | 25 | 675 | 0.34 |
| Compost | 40 | 1,080 | 0.54 |
This integrated approach ensures accurate material ordering and budget planning for any project.
Tank Volume and Liquid Capacity
Calculate practical volumes for tanks, pools, and liquid storage:
Water Tank Sizing:
| Household Size | Daily Use (gal) | 3-Day Reserve | Tank Size Needed |
|---|---|---|---|
| 1-2 people | 100-150 | 300-450 | 500 gallon |
| 3-4 people | 200-300 | 600-900 | 1,000 gallon |
| 5-6 people | 300-450 | 900-1,350 | 1,500 gallon |
Common Tank Dimensions:
| Capacity (gal) | Cylinder Dims | Cubic Feet |
|---|---|---|
| 275 (IBC tote) | 48" x 40" x 46" | 36.7 |
| 500 | 48" dia x 70" | 66.8 |
| 1,000 | 64" dia x 72" | 133.7 |
| 2,500 | 96" dia x 84" | 334.2 |
| 5,000 | 96" dia x 168" | 668.4 |
| 10,000 | 120" dia x 210" | 1,336.8 |
Swimming Pool Volumes:
| Pool Size | Avg Depth | Volume (cu ft) | Gallons |
|---|---|---|---|
| 12' round | 4' | 452 | 3,382 |
| 15' round | 4' | 707 | 5,288 |
| 18' round | 4' | 1,018 | 7,614 |
| 12' x 24' oval | 4' | 904 | 6,763 |
| 15' x 30' rect | 5' | 2,250 | 16,830 |
| 20' x 40' rect | 5.5' | 4,400 | 32,912 |
Pool Fill Costs (2026 estimates):
- Municipal water: $0.01-$0.02 per gallon
- Water truck delivery: $150-$400 per 5,000 gallons
- 15,000 gallon pool: $150-$600 to fill
Hot Tub Volumes:
| Size (persons) | Gallons | Fill Time (garden hose) |
|---|---|---|
| 2-3 person | 150-220 | 30-45 min |
| 4-5 person | 300-375 | 60-75 min |
| 6-7 person | 400-475 | 80-95 min |
| 8+ person | 500-600 | 100-120 min |
Fuel Tank Capacities:
| Tank Type | Typical Size | Gallons | Notes |
|---|---|---|---|
| Car gas tank | 10-18 gal | 10-18 | Fill to ~90% |
| Truck gas tank | 20-36 gal | 20-36 | |
| Propane (residential) | 120-500 gal | 120-500 | Fill to 80% |
| Heating oil | 275-330 gal | 275-330 | |
| Diesel (farm) | 500-1,000 gal | 500-1,000 |
Water Heater Capacities:
| Type | Capacity | Recovery Rate |
|---|---|---|
| Small tank | 30-40 gal | 30-40 gal/hr |
| Standard tank | 50-60 gal | 40-50 gal/hr |
| Large tank | 80-100 gal | 50-60 gal/hr |
| Tankless | Unlimited | 2-5 gal/min |
Practical Fill Considerations:
- Safety margins: Propane and other compressed gas tanks fill to 80% maximum
- Thermal expansion: Water expands ~4% when heated; leave headspace
- Sloshing: Moving tanks should be 85-90% full for stability
- Measurement accuracy: Dipstick readings require level surface
Excavation and Fill Volume
Calculate earth-moving volumes for construction projects:
Basic Excavation Formula:
- Rectangular pit: V = L x W x D
- Sloped sides: Use average of top and bottom dimensions
Excavation Volume Quick Reference:
| Hole Size (L x W x D) | Cubic Feet | Cubic Yards |
|---|---|---|
| 4' x 4' x 3' | 48 | 1.78 |
| 6' x 6' x 4' | 144 | 5.33 |
| 8' x 8' x 4' | 256 | 9.48 |
| 10' x 10' x 4' | 400 | 14.81 |
| 20' x 20' x 4' | 1,600 | 59.26 |
| 40' x 40' x 4' | 6,400 | 237.04 |
Trench Volume (per linear foot):
| Width x Depth | Cu Ft per Foot | Cu Yd per 10 Ft |
|---|---|---|
| 12" x 12" | 1.0 | 0.37 |
| 18" x 18" | 2.25 | 0.83 |
| 24" x 24" | 4.0 | 1.48 |
| 24" x 36" | 6.0 | 2.22 |
| 36" x 36" | 9.0 | 3.33 |
| 36" x 48" | 12.0 | 4.44 |
Swell and Shrinkage Factors:
Excavated soil increases in volume (swell), while compacted fill decreases:
| Soil Type | Swell % | Shrinkage % (when compacted) |
|---|---|---|
| Sand | 10-15% | 5-10% |
| Loam | 15-25% | 10-15% |
| Clay | 25-40% | 10-20% |
| Rock | 40-60% | 0-5% |
Example:
- Excavate 10 cu yd of clay soil
- In truck: 10 x 1.30 = 13 cu yd (30% swell)
- If re-compacted: 10 x 0.85 = 8.5 cu yd
Hauling Calculations:
| Truck Type | Level Capacity | Heaped Capacity |
|---|---|---|
| Pickup truck | 2-3 cu yd | 3-4 cu yd |
| Single-axle dump | 5-8 cu yd | 7-10 cu yd |
| Tandem dump | 10-14 cu yd | 13-18 cu yd |
| Tri-axle dump | 14-18 cu yd | 18-22 cu yd |
Cost Factors (2026):
| Activity | Cost Range |
|---|---|
| Excavation | $50-$200 per cu yd |
| Fill dirt delivery | $20-$50 per cu yd |
| Topsoil delivery | $35-$65 per cu yd |
| Disposal (clean fill) | $15-$40 per cu yd |
| Disposal (contaminated) | $100-$500+ per cu yd |
Grading and Slope:
| Slope Grade | Rise per 10' Run |
|---|---|
| 1% (min for drainage) | 1.2" |
| 2% (standard drainage) | 2.4" |
| 5% (steep walkable) | 6" |
| 10% (max for mowers) | 12" |
| 33% (1:3 slope) | 40" |
Pro Tips
- 💡Always use radius (half the diameter) for cylinder and sphere calculations. Using diameter directly gives 4x or 8x the correct volume.
- 💡Remember the 1/3 factor: cones and pyramids hold exactly one-third the volume of cylinders and prisms with the same base and height.
- 💡Convert all dimensions to the same unit before calculating. Mixing feet and inches is a common source of major errors.
- 💡One cubic yard equals 27 cubic feet. Divide cubic feet by 27 to get cubic yards for ordering construction materials.
- 💡One cubic foot holds 7.48 gallons. Multiply cubic feet by 7.48 to convert to gallon capacity for tanks and pools.
- 💡Add 5-10% extra when ordering bulk materials like concrete, gravel, or mulch to account for waste and variations.
- 💡For horizontal cylinders (like tanks), half-filled does NOT mean the liquid is at half the height due to the curved shape.
- 💡Propane and compressed gas tanks are filled to 80% capacity for safety. Account for this when planning fuel storage.
- 💡Excavated soil swells 20-40% when removed and shrinks 10-20% when compacted. Plan truck loads accordingly.
- 💡Double-check diameter vs. radius for round shapes. This single error causes the majority of volume calculation mistakes.
- 💡For irregular shapes, break them into simple shapes (boxes, cylinders), calculate each separately, and add the results.
- 💡Keep a consistent approach: always round up for material orders, but use precise values for cost estimates.
Frequently Asked Questions
Multiply length x width x height when all dimensions are in feet. Example: A box 4 ft long, 3 ft wide, and 2 ft tall = 4 x 3 x 2 = 24 cubic feet. If dimensions are in inches, multiply and divide by 1,728 to convert to cubic feet. If dimensions are mixed (feet and inches), convert everything to feet first: 6 ft 6 in = 6.5 ft. For irregular shapes, use the appropriate formula (cylinder, sphere, etc.) and input dimensions in feet.
