Nozzle Length Calculator

Plan convergent and divergent sections using practical geometry. Choose units, nozzle type, angles, and options. Get clear dimensions, charts, tables, and exports for decisions.

Calculator Inputs

Unit

Nozzle Type

Inlet Diameter

Throat Diameter

Exit Diameter

Convergent Half Angle (°)

Divergent Half Angle (°)

Straight Throat Length

Bell Percentage (%)

Wall Thickness

Estimated Flow Rate (L/s)

Include straight throat section in total length

Example Data Table

Case	Type	Inlet Diameter	Throat Diameter	Exit Diameter	Conv. Angle	Div. Angle	Throat Length	Total Length
Example A	Conical	120 mm	40 mm	140 mm	30°	15°	12 mm	274.77 mm
Example B	Bell	150 mm	50 mm	180 mm	35°	14°	15 mm	298.40 mm
Example C	Conical	90 mm	30 mm	100 mm	28°	12°	8 mm	242.27 mm

Formula Used

Convergent Length
Lc = (Rin − Rt) / tan(θc)

Equivalent Conical Divergent Length
Ld(conical) = (Re − Rt) / tan(θd)

Bell Nozzle Divergent Length
Ld(bell) = Ld(conical) × Bell Percentage

Total Nozzle Length
Ltotal = Lc + Lt + Ld

Area Ratio
Expansion Ratio = Ae / At

This calculator uses practical geometric relations for tapered nozzle sections. Conical nozzles use straight-line divergent geometry. Bell nozzles shorten the divergent section by applying a chosen percentage of equivalent conical length, then plotting a smooth contour.

How to Use This Calculator

Select your preferred unit system first.
Choose conical or bell nozzle geometry.
Enter inlet, throat, and exit diameters carefully.
Set convergent and divergent half angles in degrees.
Enter throat length if a straight section exists.
Use bell percentage only when bell geometry is selected.
Add wall thickness and flow rate for extra outputs.
Press the calculate button to display results above the form.
Review dimensions, volume estimates, ratios, and the nozzle plot.
Use the CSV or PDF buttons to export your results.

Frequently Asked Questions

1. What does this calculator measure?

It estimates convergent, throat, divergent, and total nozzle length from geometry inputs. It also reports area ratios, internal volume, material volume, and a contour plot.

2. What is the difference between conical and bell nozzles?

A conical nozzle expands with a straight taper. A bell nozzle uses a shorter, smoother divergent contour that often improves packaging and can reduce overall nozzle length.

3. Why are half angles used?

Half angle is measured from the nozzle centerline to the wall. It directly controls how quickly the radius changes and therefore sets section length.

4. Does this calculator perform full compressible flow analysis?

No. It focuses on geometric length estimation. It does not solve full thermodynamic state changes, shock behavior, or chamber performance equations.

5. What is a good use for bell percentage?

Bell percentage helps approximate a shorter bell nozzle relative to a conical equivalent. Designers often use it for compact layouts and faster early-stage sizing studies.

6. Why include throat length separately?

Many real nozzles include a short straight throat section for manufacturability or flow control. Adding it separately improves total length estimation accuracy.

7. What is residence index in this page?

Residence index is a simple internal volume divided by entered flow rate. It is a quick screening metric, not a replacement for detailed fluid simulation.

8. Can I export the results?

Yes. Use the CSV button for spreadsheet-style output or the PDF button for a clean summary document that captures the calculated values.