Propeller design with Heliciel:

The two calculators on this page use the same formulas as the Heliciel propeller design software.

On this page

Pitch and slip calculator
B-series pitch calculator
Which B-series propeller?
What propeller pitch is
B-screw series tutorial
Three worked examples
B-series models
Catalogue, or made to measure?

Propeller pitch calculator

Pitch is the distance a propeller would advance in one revolution if it turned in a solid nut instead of water or air. Everything else about a propeller — the speed it will reach, the rpm the engine will settle at, the efficiency it will deliver — follows from that one length. The two free calculators below answer the two questions people actually ask about it: what is my propeller really doing? and what pitch should it have? Further down you will see what a propeller designed for your own duty does that a catalogue one cannot.

1. Prop pitch and slip calculator

You know your propeller and you have measured your speed. This prop pitch calculator gives you the theoretical speed, the slip, and the pitch you would need to reach a different speed at the same rpm.

Propeller pitch inches Engine speed at that point rpm Gearbox reduction ratio 1 for a direct drive Measured boat speed Speed you are aiming for optional, same unit

Fill in the fields and press the button.

Two propellers of the same diameter and different pitch do not do the same job. A lower pitch lets the engine reach its rated rpm and pulls harder at low speed — water skiing, heavy loads, a hull that has to climb onto the plane. A higher pitch gives a higher top speed for the same rpm, but if it is too high the engine never reaches its rated speed, it labours, and it burns more fuel for less thrust.

Propeller pitch formula

Propeller rpm = engine rpm ÷ gearbox ratio. Theoretical speed = pitch × propeller rpm: with the pitch in metres and the rpm per minute you get metres per minute, which becomes knots when multiplied by 60 and divided by 1,852. Slip = 1 − measured speed ÷ theoretical speed. Conversely, the pitch you need for a target speed, at the same rpm and the same slip, is target speed ÷ (propeller rpm × (1 − slip)). The calculator above applies these three formulas, unit conversions included.

2. Wageningen B-series pitch calculator

The slip calculation above tells you what a propeller you already own is doing. It does not tell you what a propeller could do. For that you need measurements — and the most widely used set of measurements in marine propulsion is the Wageningen B-screw series: dozens of model propellers built and towed in the Netherlands, varying only the number of blades, the blade area and the pitch.

This calculator evaluates the Oosterveld and van Oossanen regressions of that series (Carlton, Marine Propellers and Propulsion, Table 6.6, Re = 2×10⁶) — 39 terms for the thrust coefficient K_T, 47 for the torque coefficient K_Q. It gives the geometric pitch of the propeller, the advance ratio at which it is most efficient, and the efficiency it reaches there.

Number of blades Z Blade area ratio Ae/A0 values actually measured for this blade number Pitch ratio P/D 0.60 to 1.40 Propeller diameter mm Shaft speed rpm — optional

Choose a geometry.

Open-water diagram of the selected series: K_T, 10 K_Q and efficiency against advance ratio J. The dot marks the point of maximum efficiency.

Outside the range of the series — P/D below 0.60 or above 1.40, blade area ratio below 0.30 or above 1.05 — this calculator refuses to answer and says why. The regression was fitted to a finite set of towing-tank measurements; extrapolated beyond them it would return a number, but not a measurement. The Heliciel software applies the same rule.

3. Which B-series propeller for your boat?

The two calculators above start from a propeller. This one starts from your requirement: the diameter the hull allows, the thrust you need, the speed of advance. It then sweeps the whole B-series — the 21 tabulated geometries from 3 to 7 blades, and for each of them the 81 pitch ratios from 0.60 to 1.40 — and names the propeller that delivers that thrust at the best efficiency, together with the shaft speed it requires.

Propeller diameter mm — the largest the hull allows Required thrust N Speed of advance m/s Fluid Density kg/m³ — editable

Enter your requirement and press the button.

How the rpm comes out when you never supplied it

This is the part that surprises: you look for a propeller without knowing how fast it will turn. It works because of one quantity that does not contain the rpm — the load coefficient:

K_T / J² = T / (ρ V² D²) — where T is thrust, ρ the fluid density, V the speed of advance and D the diameter.

For every geometry in the series the calculator solves K_T(J) = load × J². The root is unique: K_T falls from its bollard-pull value to zero while load × J² rises from zero. From that J follow the shaft speed, the torque, the shaft power and the efficiency. Series unable to deliver the requested thrust at any pitch are ruled out and counted: none of them disappears silently.

This is exactly the method of the Best propeller tab of the Heliciel software, with the same bounds and the same sweep step: the name returned here is the one the software returns.

One consequence worth knowing: because the ranking is on efficiency alone, the narrowest blade of each family almost always wins — a thin blade drags less. Yet blade area is precisely what protects against cavitation, and this calculation does not check it. A propeller that has to work for a living usually needs a more generous blade area ratio than the pure efficiency optimum. Read the runners-up, and watch the blade tip speed: that is what gives away an impossible shaft speed.

What propeller pitch actually is

This section is a summary. The article Propeller pitch: geometric and effective pitch develops these notions, variable pitch propellers shows how pitch is changed in operation, and apparent velocity and angle explains why a blade is twisted.

Geometric pitch

A propeller blade is a piece of helical surface. Extend that helix for one full turn and the distance it travels along the shaft is the geometric pitch P, quoted in millimetres or in inches. A 14 × 19 propeller is 14 inches in diameter with a 19 inch pitch: one turn, 19 inches forward — in theory.

Pitch ratio P/D

Divide the pitch by the diameter and the units disappear: P/D is the same number for a model and for the full-size propeller it represents. That is why every propeller series is catalogued by pitch ratio rather than by pitch, and why the B-series calculator above asks for P/D and a diameter separately. Typical values run from 0.6 on a heavily loaded tug propeller to 1.4 on a fast planing hull.

Blade pitch angle

At a radius r, the blade section is set at an angle φ such that tan φ = P / (2πr). The pitch is constant along the blade in this definition, so the angle is steep at the root and shallow at the tip. Quoted pitch angles usually refer to the section at 70 % of the radius, which is representative of the blade as a whole.

Slip

Water is not a nut. The propeller has to push water backwards to generate thrust, so it never advances by its full pitch: the shortfall is the slip. Slip is not a loss to be eliminated — a propeller with zero slip would produce zero thrust. It is simply the sign that the propeller is working.

Advance ratio J

The dimensionless form of the same idea: J = V / (n D), where V is the speed of advance, n the revolutions per second and D the diameter. Every open-water chart, including the one drawn above, is plotted against J. A propeller has one J at which it is most efficient; matching that J to the speed and rpm of your boat is the whole job of propeller selection.

The B-screw series tool in Heliciel, step by step

The calculator above works on one geometry at a time. The Basic blade models window of the Heliciel propeller design software does the rest: it sweeps the entire series, builds the blade, and hands the result to a blade element momentum (BEM) calculation that accounts for your actual fluid, speed and rpm.

Step 1 — the three numbers that define a B-series propeller

On the left of the window you set the diameter in millimetres, the number of blades from 3 to 7, and you pick a blade area ratio from the list belonging to that blade number. These lists are not free: they hold the ratios that were actually built and towed — 0.35, 0.50, 0.65 and 0.80 for a three-bladed propeller, 0.40 to 1.00 for a four-bladed one, and so on. The pitch ratio P/D is typed in its own box, between 0.60 and 1.40.

Step 2 — read the operating point

The Optimal operating point panel updates as you type. It shows the pitch ratio, the pitch in millimetres for the diameter you entered, the advance ratio J at maximum efficiency, the efficiency itself, and that J translated into a speed of advance at 100, 500 and 1000 rpm. Those three rpm figures are reading aids, not properties of the series: the B-series is dimensionless and holds at any speed. They are there to turn an abstract J into a speed you can recognise.

Step 3 — let the software find the propeller

The Best propeller tab reverses the question. You give it the diameter you can fit, the thrust you need, the speed of advance, and the fluid of your project — and it returns the propeller of the series that delivers that thrust at the highest open-water efficiency, together with the shaft speed it requires.

It can do that without knowing the rpm because of one quantity that does not contain it: the load coefficient K_T / J² = T / (ρ V² D²). For every combination of blade number, area ratio and pitch ratio — the pitch being swept from 0.60 to 1.40 in steps of 0.01 — the software solves K_T(J) = load × J², deduces the rpm, the torque, the power and the efficiency, and ranks the lot. Series that cannot produce the requested thrust at any pitch are listed with the reason rather than quietly dropped.

Step 4 — turn the selection into a blade

Three buttons carry the result into the project:

Chord distribution — the blade outline of the series, and nothing else. Your own profiles and pitch settings are kept.
Chords and profiles — the outline plus the segmental and aerofoil sections of the series, with their thickness law.
Chords, profiles and pitch settings — the complete geometry, including the blade twist that corresponds to the selected P/D. This is the reverse-engineering mode: the project now is that B-series propeller.

From there the propeller is an ordinary Heliciel project, and that is where it stops being a catalogue propeller. The BEM calculation gives thrust, torque, power and efficiency for your fluid, your speed and your rpm — not for the towing tank's. And every part of the geometry the series had frozen becomes yours again: you can change the profile of any blade element, let the software recompute the optimal twist for your operating point, and reshape the chord distribution. The B-series selection is then what it should be — a sound starting point, not the finished propeller. See catalogue, or made to measure? below.

Three worked examples

A planing boat — high pitch, small blade area

A 6 m planing hull, 400 mm propeller, cruising at 12 m/s and needing about 2 500 N of thrust. The load coefficient is low: the hull is fast and light for the disc area available. The series answers with few, narrow blades and a high pitch ratio — the family around B3-35 to B4-55, P/D between 1.0 and 1.3. Enter B4-55 with P/D 1.20 and a 400 mm diameter in the calculator above: pitch 480 mm, best efficiency near 70 %, reached at J ≈ 0.98, that is 12 m/s at about 1 830 rpm at the shaft.

A displacement sailing yacht — low pitch, moderate area

Ten tonnes, 5 knots under engine, a 450 mm propeller in an aperture. Speed is low and thrust is high, so the load coefficient is large and the optimum moves the other way: three blades, area ratio 0.50 to 0.65, P/D between 0.7 and 0.9. Efficiency is lower than on the planing boat — that is the price of pushing a heavy hull slowly, not a mistake in the selection.

A pusher tug — maximum blade area

Thrust at very low speed, the propeller heavily loaded and cavitation the limiting factor. Blade area is what keeps the pressure on the back of the blade above the vapour pressure, so the selection moves towards four or five wide blades, Ae/A0 from 0.85 to 1.05, P/D around 0.6 to 0.8. Try B5-105 at P/D 0.75 in the calculator: efficiency falls to about 55 %, and that figure is honest — a bollard-pull propeller is not a fast-boat propeller.

The efficiencies above are open-water figures for the bare propeller: they take no account of the hull in front of it, of the wake it works in, or of the shaft and bracket behind it. They are the right number for comparing propellers with each other, and an optimistic one for predicting the speed of a boat.

B-series propeller models

Turn a model with the mouse, read its characteristics in the data sheet, download the Heliciel project to open and modify it. B-series propellers are being added to it as they are produced.

Heliciel builds the 3D model of any Wageningen B-series propeller from its Basic blade models window and exports it as STL, IGES or STEP for 3D printing, CAD import or a CFD mesh. Heliciel STL exports are in metres: if your CAD software opens the propeller at one thousandth of its size, set the import unit to metres.

These models are ready-made propellers picked from a catalogue. Their outline, their blade sections and their twist are those of the series, decided once and for all in a towing tank in the Netherlands. Take the one whose characteristics are closest to your project, print it, mesh it, bolt it on: it will work, and it will work at the efficiency the series gives — no more.

A catalogue propeller, or one made for your job?

The series contains a finite number of geometries, and yours is almost certainly not one of them. You pick the nearest, and the gap between that propeller and the one your project actually calls for is paid every hour the machine runs, in fuel or in battery.

What the gap is made of is worth spelling out. A series propeller has one pitch law for the whole family: essentially constant along the radius, with a reduction near the root on the higher blade numbers. But a blade does not meet the same flow at every radius — the rotational speed grows in proportion to the radius, the induced velocities vary, the local Reynolds number changes from root to tip. A single pitch law cannot put every section of the blade at its best angle of attack. Some sections work well, the others drag along.

That is exactly what a blade element momentum calculation removes. Heliciel divides the blade into elements, computes the flow each one actually sees at your operating point, and sets the twist of each element so that its profile works at the incidence you ask for — typically the one giving the best lift-to-drag ratio for that profile, at that local Reynolds number. The blade is no longer a fixed helix: it is a twist law computed for your speed, your rpm, your fluid and your diameter.

And the sections themselves become a choice. The B-series imposes its own segmental and aerofoil profiles. Heliciel lets you assign a profile to each element, taken from a database of aerofoils with their polars, or one of your own — thick and tolerant at the root where the blade has to carry the bending, thin and efficient at the tip where the speed is highest.

What is fixed, and what you can still decide
	B-series model catalogue propeller	Heliciel design made to measure
Blade outline	fixed by the family	free, and optimizable
Blade sections	those of the series	chosen element by element, with their polars
Twist	the pitch law of the family	computed element by element for your operating point
Operating point	one advance ratio	your speed, rpm, fluid and immersion
Reynolds number	2×10⁶, the towing tank's	the one your propeller actually works at
Off-design behaviour	not described	performance maps over speed and rpm
Cavitation, structure	not covered	checked on your blade
Result	a geometry to copy	STL, IGES, STEP, OBJ — and CFD in the PRO version

The honest way to use this page is therefore in two steps. Use the calculators above to size the problem: how much pitch, how many blades, how much blade area, what efficiency a known propeller reaches on your duty. Then, if the machine is going to run for years, design the propeller for that duty rather than borrow one that was designed for another.

Heliciel starts exactly where the series stops: blade element momentum calculation on your own fluid and operating point, free choice of aerofoil sections with their polars, optimal twist for each element, genetic optimization of the chord distribution, the blade number, the diameter and the rpm, cavitation check, structural check of the blade, performance maps — and, in the PRO version, a full CFD calculation of the propeller you have just designed.

Design your own propeller with Heliciel

Frequently asked questions

How do I calculate propeller pitch from rpm and speed?

Divide the engine speed by the gearbox ratio to get the propeller speed, then divide your speed of advance by that: the result is the distance travelled per revolution. Divide it by one minus the slip and you have the pitch. The first calculator on this page does exactly that, with the unit conversions handled for you.

What is a normal slip figure?

Between 10 and 20 % for a correctly propped motorboat, less on a fast, light hull, considerably more on a displacement hull or a heavily loaded working boat. These are rules of thumb, not measurements: slip changes with load, trim and rpm on the same boat.

Should I change diameter or pitch?

Diameter first: it has far more influence on thrust and efficiency than pitch, and it is usually limited by the tip clearance the hull allows. Once the diameter is fixed at the largest value that fits, pitch is what sets the rpm the engine will reach.

Is the Wageningen B-series suitable for my propeller?

It was developed for marine propellers of conventional shape, with segmental and aerofoil sections, operating without cavitation at a Reynolds number of 2×10⁶. It is an excellent starting point for a boat propeller and a poor one for an air propeller, a wind turbine or a ducted fan — those need blade element momentum calculation with aerofoil polars of their own, which is what the Heliciel software is for.

Does this calculator replace a design?

No. It gives you the pitch and the efficiency of a known family of propellers — a catalogue geometry, frozen in a towing tank decades ago. It does not choose the profile of your blade sections, it does not compute the twist that would put each of them at its best angle of attack on your duty, it does not check cavitation at your immersion depth, and it does not tell you what happens away from the best efficiency point. Those are design questions, and they are what the Heliciel software answers.