Rip Rap Calculator

Size rip rap stone from water velocity, then estimate volume, weight and cost.

Two Isbash turbulence constants, metric and imperial units, and 113 currencies for pricing.

Updated October 23, 2026

CreatorFrank Zhao

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Introduction

Rip rap is a layer of loose stone laid over a bank, a channel bed or an outfall so that moving water meets rock instead of soil. This page answers the two questions that decide whether that layer does its job: how large the individual stones have to be, and how much stone the job needs.

The stone-size half of the page works from water velocity. You give it the fastest flow the lining will face, the turbulence of that flow and the specific gravity of the stone, and it returns the average stone size — the diameter written as D50. The quantity half works from the shape of the job: an area and a layer depth become a volume, a wastage allowance turns that into the volume to order, the stone density turns the order into a tonnage, and a price per unit mass turns the tonnage into money.

The first card on the page asks which of the two you are working out, because the groups below it change with your answer. Choosing the third option shows both at once, which is the usual case: the stone size decides the layer thickness, and the thickness is what you order. That link matters in practice — a layer has to be at least two stones deep, so a stone size of 13.83 cm sets the minimum layer at 27.66 cm before any allowance is added.

Contractors armouring a drain outfall, landscape crews rebuilding a washed-out bank, and engineers checking whether the stone a quarry can deliver is coarse enough for a channel all start in the same place: a velocity on one side, an order on the other. What this page does not do is design the whole revetment — the filter layer, the toe and the bank stability are outside it, and the notes at the end say so plainly.

D50 in five units

Millimetres, centimetres, metres, inches or feet

1,600 kg/m³ floor

Lighter stone is flagged, never hidden

113 currencies

Price per kilogram, ton, pound, stone or US ton

Quick start

Say which answer you need

The first card offers three choices: the average rock diameter, the rip rap volume, or both. Pick the diameter when you know the velocity and need a stone size. Pick the volume when the stone is already specified and you only need quantities. Pick both when the layer thickness has to follow from the stone, which is the normal case for a new lining. Numbers you have already typed stay with their group when you switch between the three.

Enter the velocity the lining has to survive

This is the average approach velocity in the stone-size formula. Type it in whatever unit you measured it — m/s, km/h, ft/s, yd/s, mph or ft/min — and the page converts it before any arithmetic. The page applies no safety factor of its own, so the number you enter should already be the fastest flow the lining is meant to take, not a quiet-day reading.

Choose the turbulence constant

Two values are offered: 0.86 for highly turbulent flow, which is the page’s opening choice, and 1.2 for low turbulence. Because the constant is squared in the denominator, the choice matters twice over: on the same water, 0.86 asks for nearly double the stone that 1.2 does. The comparison is worked through below.

Enter the specific gravity of the available stone

The page accepts 2.5 to 3.0 and flags anything outside that band. It is a property of the rock itself, so it comes from the supplier’s test result rather than from a general assumption about “stone”.

Read the stone size and check the layer depth

The average rock diameter appears in the unit its menu is set to, and it is the size you specify, not the largest stone in the load. A layer needs at least two stones of depth, so the thickness you enter later has to be at least twice this diameter; the page flags both boxes when it is not.

D_{50}

=

\frac{V^{2}}{2\,g\,C^{2}\,(S-1)}

=

\frac{2.5^{2}}{2 \times 9.806 \times 1.2^{2} \times (2.6-1)}

=

13.83\ \mathrm{cm}

With a specific gravity of 2.6 at low turbulence, 2.5 m/s asks for 13.83 cm stone, so the layer must be at least 27.66 cm thick — a 30 cm layer covers it with a small margin.

Turn the layer into an order

Enter the area to cover, the layer depth, the wastage allowance (5% is already filled in) and the bulk density of the delivered stone (1,680 kg/m³ is the opening value). The page returns the layer volume, the volume to order, the total volume including the allowance, the weight and, once you enter a price, the rock cost.

The weight box is the one to hand to a quarry that sells by the ton. If you would rather start from a quantity — a truckload you already paid for, or a budget that will not move — type it into the volume, weight or cost box and the page works backwards instead.

Read the colours the same way every time

A box that the page solved turns blue. A red box keeps its number and adds a sentence explaining which boundary it crossed, so you can see the result and the objection together; a box left empty is simply waiting for an input it needs.

The formulas behind the results

Stone size: the Isbash form

The diameter comes from a single statement that balances the drag of the flow against the weight of a stone resting on the bank:

D_{50} = \frac{V^{2}}{2\,g\,C^{2}\,(S-1)}

D_{50}

Average rock diameter

The size half the stones are smaller than and half larger than, which is why it is a median rather than an extreme. The menu changes the unit it is shown in and nothing about the calculation.

V

Average approach velocity

The velocity of the water arriving at the lining. Whatever unit the menu shows, the arithmetic reads metres per second.

g

Gravitational acceleration

9.806 m/s² unless you change it. The box is open so you can use the value your project specifies or try another rounded figure.

C

Turbulence constant

0.86 for highly turbulent flow or 1.2 for low turbulence. It is squared in the denominator, so the setting counts twice in the result.

S

Specific gravity of the stone

The rock’s density relative to water. The page accepts 2.5 to 3.0, which is where rip rap stone normally sits.

Why the turbulence constant counts twice

Because it is squared, a change from 0.86 to 1.2 changes the stone size by a factor of $(1.2/0.86)^{2} \approx 1.95$ . At 2 m/s over stone of specific gravity 2.6, highly turbulent flow asks for 17.24 cm and low turbulence asks for 8.85 cm on the same velocity: nearly double the stone for the same water. Deciding whether the flow is rough or smooth is therefore a bigger decision than the third decimal of the velocity.

The reverse answers

Four of the five boxes can be the unknown: the velocity, the acceleration, the specific gravity and the diameter. The turbulence constant is a setting with two published values, not a value the page will work out. The useful direction is the velocity, because it turns the page into a check on stone you can actually buy:

V

=

C\sqrt{2\,g\,(S-1)\,D_{50}}

Type a stone diameter you have seen in the quarry’s stockpile and the page returns the fastest water that stone is good for. The acceleration and the specific gravity can be solved the same way, though those are rarely the number you are missing.

Opening values, and what they assume

The following sizes come from the same statement as the page, at its opening turbulence constant of 0.86, a specific gravity of 2.6 and standard gravity. They are rounded to two decimals; changing the turbulence constant or the specific gravity moves every row.

Velocity (m/s)	D50 (cm)	Minimum layer (cm)
1.0	4.31	8.62
2.0	17.24	34.47
3.0	38.78	77.56
4.0	68.94	137.88
5.0	107.72	215.44

What a median size does and does not tell you

D50 describes the middle of the stone in the layer. A real gradation has a top size as well, and the page has no separate box for it — so treat the result as the size to specify as the median and have the supplier’s gradation checked separately, rather than as a limit on the largest stone allowed.

Volume, allowance, weight and cost

The quantity half is four ordinary multiplications. The area is multiplied by the layer depth to give the volume of the layer:

V_{\mathrm{r}} = A \times d

The wastage allowance is a share of that volume, so the order volume is the layer volume grown by the allowance, with 5% entering the arithmetic as 0.05:

V_{\mathrm{t}} = V_{\mathrm{r}} \times \left(1 + w\right)

Weight comes from the bulk density of the delivered stone — the density of the pile, including the air between the stones, not the density of a solid block of rock:

W = V_{\mathrm{t}} \times \rho

And the cost is the weight multiplied by the price per unit mass. The price box carries two menus of its own — one for the currency and one for the mass unit the quote is written in — because a quarry quote is usually per ton while a bag price is per kilogram or per pound:

C_{\mathrm{cost}} = p \times W

All four statements solve in either direction. Typing a total volume returns the area or the depth, typing a weight returns the volume to order, and typing a budget returns the price per ton or the tonnage it buys — the box you last edited becomes the input and one of its neighbours is solved from it.

If the lining sits on a gravel bedding or filter layer, that layer is a second area-by-depth calculation of its own; the gravel calculator does the same volume, tonnage and cost arithmetic with the bulk densities of gravel and crushed stone.

Worked examples

Checking stone that is already on site

Situation: A quarry has 30 cm rip rap in stock and a channel that peaks at 2.4 m/s. Before the load is tipped, the question is whether that stone is coarse enough, not how big the stone should be.

Inputs

Average rock diameter30 cm

Turbulence constant0.86 (highly turbulent)

Specific gravity2.6

Result

V

=

0.86\sqrt{2 \times 9.806 \times (2.6-1) \times 0.30}

=

2.64\ \mathrm{m/s}

The same stone also sets the layer. Two stones deep is 60 cm, so the page will only clear a layer of 60 cm or more for a stone this size.

In practice: The stone's ceiling is above the 2.4 m/s the channel is expected to reach, so it sits inside the range rather than beyond it. A flow above 2.64 m/s is more than this calculation says the stone will hold — that is the number to compare with the flow you are designing for.

From square metres to a delivered tonnage

Situation: A 240 m² section of bank is to be lined 30 cm deep with the stone from the first example. The quarry sells by the metric ton at 45 USD per ton, and the load travels a long way, so the order is not to be short.

Inputs

Area240 m²

Depth30 cm

Wastage5%

Bulk density1,680 kg/m³

Price45 USD per metric ton

Result

V_{\mathrm{r}}

=

240 \times 0.30

=

72\ \mathrm{m^{3}}

V_{\mathrm{t}}

=

72 \times 1.05

=

75.6\ \mathrm{m^{3}}

W

=

75.6 \times 1{,}680

=

127.008\ \mathrm{t}

C_{\mathrm{cost}}

=

127.008 \times 45

=

5{,}715.36\ \mathrm{USD}

In practice: Order the tonnage, not the volume, if the quarry quotes by weight: 127.008 t plus whatever the supplier rounds to. The allowance is the only slack in the calculation — it covers spillage and an uneven subgrade, not a change of layer thickness.

Getting values you can defend

Start from the velocity you cannot avoid

The stone-size result is only as good as the velocity entered. Use the highest flow the lining is meant to survive across its design life rather than a measured average from a calm day, because the page itself adds no safety margin.

Two stones is the minimum layer, not a target

The page flags a layer thinner than twice the stone diameter because a single stone of thickness has nothing to interlock with. If the depth box goes red, either thicken the layer or choose a smaller stone — thickening the layer is often the simpler change to a section that is already staked out.

Take the density from the load, not the rock type

The tonnage is computed from the bulk density of the delivered stone, which is lower than the density of the solid rock because it counts the voids. A density under 1,600 kg/m³ is flagged: it is almost always a specific gravity typed into the box.

Match the price to the quote's unit

45 per metric ton and 0.045 per kilogram are the same money. The price box remembers its own mass unit, so check that the unit shown next to the price matches the quote before reading the cost; a mismatch shows up as a cost out by a factor of a thousand.

The allowance is a construction buffer, not a design factor

Five percent covers spillage, losses in handling and an uneven subgrade. It does not thicken the layer, and it is capped at 20% because a larger figure is nearly always a quantity typed into a percentage box rather than an allowance.

Questions

Why does the low-turbulence setting give a smaller stone?

The turbulence constant sits in the denominator and is squared. $C = 1.2$ is larger than $C = 0.86$ , so the denominator grows and the required diameter shrinks by roughly $(1.2/0.86)^{2}$ , about 1.95 times. Smoother water needs less stone; rough, turbulent water needs more.

Can I start from the stone size instead of the velocity?

Yes. Type the diameter into the average rock diameter box and the velocity box is solved for you — that is the fastest flow the stone is good for. The acceleration and the specific gravity can be solved from the same set of numbers if one of those is the value you are missing.

Why did the depth box turn red when everything else looks fine?

Because the layer is thinner than two stones. With a 13.83 cm stone the depth has to reach 27.66 cm; the page marks both the depth and the stone size so the pair is obvious. Thicken the layer, or size the job around a smaller stone.

Why did my area change when I typed a volume?

Both directions of every statement are live. The box you typed is the input, and one of its neighbours is solved from it — so a volume with a depth already in place returns a new area. If the area is the value you trust, retype it (or clear the volume) and the page will solve the volume instead.

What wastage should I use?

5% is a reasonable default for a machine-placed layer on a prepared subgrade. Raise it for rough ground, hand placement or a long haul where losses are harder to control; the page accepts up to 20%, which adds a fifth to the measured volume.

How far the result goes

The stone size comes from a simplified empirical statement for steady flow over a lining. That is the right shape of calculation for an early check and a sensible starting point for a quotation, but it is not a substitute for the design criteria a real scheme is reviewed against.

The model is a single velocity and a single stone size. Waves, boat wash, ice, floating debris, sharp bends, secondary currents, bridge constrictions and toe scour are not in it, and it applies no factor of safety.
The bank slope, the height of the bank above the water, the filter or geotextile layer under the stone and the shape of the toe are outside the calculation. The page gives you stone and quantities, not a complete revetment section.
The diameter is a median for the layer. The gradation the supplier actually delivers — top size, the proportion of fines, how angular the stone is — decides how it behaves in place, and none of that is an input here.
Volume is pure geometry: a level layer of uniform depth. Uneven ground, compaction and bulking after transport are covered only by the wastage allowance you choose.
The cost is stone only. Haulage, plant and labour, erosion control fabric, permits and tax are all separate, and a price converted from another currency moves with the exchange rate after the quote date.
The page is an estimate for planning and procurement. For a lining that protects property, or that sits in a channel whose failure would matter, have the velocity, the stone size and the layer thickness reviewed by a qualified engineer against the criteria that apply on your site before work starts.

None of that makes the answer unusable — it makes it a starting number with a known edge. The sizes and quantities here are good enough to compare options, price a job and notice when a supplier’s stock is likely to be too fine.

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