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Mechanical Engineering3D

Pressure Vessel Volume Calculator

Calculate internal volume of horizontal/vertical pressure vessels including cylindrical shell and 2:1 elliptical heads.

Inputs
Enter your values below
Result
Total Vessel Volume
—
Enter values and click Calculate
Formula
π × (diameter ÷ 2)² × height × 1000 + π × diameter³ ÷ 12 × 1000
Result unit: L

Shell volume = π(D/2)² × L. Two 2:1 elliptical heads ≈ 2 × (πD³/24) = πD³/12. ×1000 converts m³ to liters.

Introduction

Calculate the total internal volume of a pressure vessel including the cylindrical shell and two 2:1 elliptical ASME heads. Enter the vessel diameter and shell length (tangent-to-tangent) to get volume in liters, cubic meters, and gallons. This calculator follows ASME BPVC Section VIII practice for 2:1 elliptical head volume (V_head = pi x D^3 / 24) and is used for vessel sizing, capacity planning, reactor volume estimation, and separator design. Shell volume uses V = pi x (D/2)^2 x L with the straight tangent-to-tangent length; head volume is added automatically.

How This Calculator Works

Shell volume = π(D/2)² × L. Two 2:1 elliptical heads ≈ 2 × (πD³/24) = πD³/12. ×1000 converts m³ to liters.

Total vessel volume = Shell Volume + 2 x Head Volume. Shell Volume = pi x (D/2)^2 x L. Each 2:1 Elliptical Head Volume = pi x D^3 / 24. The calculator uses D and L in meters and converts to liters (x1000). For other head types (hemispherical, torispherical), use the Pressure Vessel Engineering Hub reference tables.

Step-by-step process:

  1. Enter your input values in the calculator above
  2. The engine converts all inputs to SI base units (meters, kg, Pa)
  3. The formula is evaluated: pi * (diameter/2)^2 * height * 1000 + pi * diameter^3 / 12 * 1000
  4. Result is formatted with the appropriate unit and precision

Calculation Example

2m × 5m shell (15,708 L) + two heads (~2,094 L) = ~17,800 liters total.

Inputs: diameter=2, height=5
Result: 17802 L

Head Types and Volume Formulas

2:1 Elliptical (ASME standard, most common): V = pi x D^3 / 24 per head. Head depth = D/4.

Hemispherical: V = pi x D^3 / 12 per head. Head depth = D/2.

Torispherical (ASME F&D): V ≈ 0.10 x D^3 per head (approximate, depends on knuckle radius).

The engine uses the 2:1 elliptical head volume. For hemispherical heads multiply the head allowance by 2; for torispherical heads use about 0.10 x D^3 per head for preliminary estimates.

Worked Example: 3 m x 8 m Horizontal Vessel

Inputs: D = 3 m, shell length L = 8 m (tangent-to-tangent), 2:1 elliptical heads.

Shell volume = pi x (1.5)^2 x 8 = 56.55 m3.

Two heads = pi x 27 / 12 = 7.07 m3. Total = 63.62 m3 = 63,620 liters = 16,805 US gallons.

The two 2:1 heads add about 12.5% to the shell volume at L/D = 2.67.

Unit Conversion Reference

Volume: 1 m3 = 1,000 liters = 264.17 US gallons = 35.315 ft3 = 220.0 UK gallons.

To convert liters to US gallons multiply by 0.2642. A 17,802 L vessel = 4,702 US gallons.

1 US gallon = 3.785 liters; 1 ft3 = 28.32 liters.

Vessel Sizing Considerations

Common pressure vessel proportions: L/D (tangent-to-tangent) from 2.5 to 5 for horizontal separators; vertical vessels often sized by required liquid hold-up time.

Operating fill is typically 80-90% of total volume for liquid service; gas service uses the remaining vapor space.

Nozzle and internal volumes are normally ignored (less than 1% of total). The 2:1 elliptical head depth is D/4, so overall length = T/T length + D/2.

Shell Volume Per Meter Reference

For quick capacity checks, remember the shell volume per meter of length for common diameters (shell only, V/m = pi x (D/2)^2):

D = 1.0 m: 0.785 m3/m (785 L/m).

D = 1.5 m: 1.767 m3/m (1,767 L/m).

D = 2.0 m: 3.142 m3/m (3,142 L/m).

D = 2.5 m: 4.909 m3/m (4,909 L/m).

D = 3.0 m: 7.069 m3/m (7,069 L/m).

D = 4.0 m: 12.566 m3/m (12,566 L/m).

To include 2:1 elliptical heads, add pi x D^3 / 12 for the pair (about 0.21 x D^2 per meter at L/D = 1). A 3 m diameter vessel with 6 m shell: 7.069 x 6 + 7.07 = 49.48 m3, matching the worked example above.

Engineering Applications

  • •ASME pressure vessel sizing and capacity
  • •Chemical reactor volume estimation
  • •Compressed gas storage vessel design
  • •Separator and scrubber capacity planning
  • •Process vessel sizing for plant design
  • •Liquid hold-up time and operating volume checks

Frequently Asked Questions

How do you calculate pressure vessel volume?

Vessel volume = Shell Volume + 2 x Head Volume. Shell = pi x (D/2)^2 x L. For 2:1 elliptical heads: V = pi x D^3 / 24 (per head). Example: 2m diameter, 5m shell length: V = pi x 1^2 x 5 + 2 x pi x 8/24 = 15.71 + 2.09 = 17.80 m3 = 17,802 liters.

What is the volume of a 2:1 elliptical head?

A 2:1 elliptical head volume = pi x D^3 / 24 per head. For a 2m diameter vessel, each head = pi x 8/24 = 1.047 m3 (1,047 liters). Two heads add 2,094 liters to the total vessel volume.

What is the difference between shell volume and total vessel volume?

Shell volume is the straight cylindrical section only: V_shell = pi x (D/2)^2 x L. Total vessel volume includes shell + 2 heads. For 2:1 elliptical heads, heads add approximately 21% to shell volume when L = D.

How do I convert vessel volume to gallons?

1 m3 = 1,000 liters = 264.17 US gallons. Multiply liters by 0.2642 for US gallons. A 17,800 liter vessel holds approximately 4,702 US gallons.

What head type does this calculator use?

This calculator uses 2:1 elliptical heads (ASME standard), the most common head type for pressure vessels. For hemispherical heads (pi x D^3/12) or torispherical (approx 0.1 x D^3), see our Pressure Vessel Engineering Hub for reference tables.

What is the formula for ASME vessel volume with heads?

V_total = pi x (D/2)^2 x L + 2 x (pi x D^3 / 24). This gives volume in m3. Multiply by 1000 for liters. For a 3m diameter, 6m shell: V = pi x 2.25 x 6 + 2 x pi x 27/24 = 42.41 + 7.07 = 49.48 m3 = 49,480 liters.

How do I find the volume of a horizontal cylinder with liquid at a partial level?

This calculator gives total vessel volume. For partial liquid level in a horizontal cylinder you need the segment-area integration V = L x A(segment) (or a partial-fill table). Use our Liquid Volume Calculator for partially filled tanks and cylinders.

What is the difference between T/T length and overall length?

Tangent-to-tangent (T/T) length is the straight cylindrical shell only. Overall length adds both head depths: for 2:1 elliptical heads each head depth is D/4, so overall = T/T + D/2. Enter the T/T length in this calculator; head volume is added automatically.

Do nozzles and internals affect the volume?

Nozzles, baffles, and internal piping typically occupy well under 1% of vessel volume and are ignored for sizing purposes. For ultra-accurate hold-up calculations, subtract major internal hardware volume explicitly.

What is the volume per meter of shell for common vessel diameters?

Shell volume per meter (V/m = pi x (D/2)^2): 1.0 m diameter = 0.785 m3/m, 1.5 m = 1.767 m3/m, 2.0 m = 3.142 m3/m, 2.5 m = 4.909 m3/m, 3.0 m = 7.069 m3/m, 4.0 m = 12.566 m3/m. Multiply by shell length, then add two 2:1 heads (pi x D^3 / 12) for total vessel volume.

How do I size a vessel for a required liquid hold-up time?

Required volume = liquid flow rate x hold-up time. For a 5 m3/h liquid and 10 minutes of hold-up, you need about 0.83 m3 of working liquid volume; at 80% operating fill that means roughly 1.04 m3 total. Then select a standard diameter and solve for shell length using this calculator.

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Engineering Disclaimer: Calculations are for reference and educational purposes only. Always verify results independently for engineering design. See full disclaimer.
Reviewed by: Industrial Engineering Team
References: ASME B31.3, ASTM A36, Perry's Chemical Engineers' Handbook