Riprap Calculator - D50 Stone Size & Tonnage Tool

Riprap erosion control calculator

Riprap is loose rock placed on a slope, channel bed, or shoreline to stop erosion. The riprap erosion control calculator works out how much rock a project needs: the required stone size, the volume of rock, and the tonnage to order, based on the project's dimensions, slope angle, and water flow condition.

What riprap does

Erosion happens when moving water pulls soil particles away from a bank, slope, or channel. Riprap fights this by covering the soil with heavy, angular rock. The rocks lock together and let water pass through the gaps between them, so the layer absorbs the force of the flow instead of the bare soil underneath.

Engineers describe a riprap layer by its D50, the median stone size. Half the stones in the mix weigh more than the D50 size and half weigh less. D50 matters more than the biggest stone in the pile, because riprap works as a group: smaller stones fill the gaps between larger ones, and that interlocking is what keeps the whole layer from sliding or washing away.

Riprap shows up around culvert outlets, along stream banks, under bridge piers, on channel linings, and on shorelines exposed to waves.

How the calculator works

The calculator takes four inputs: length, width, and depth of the area to be covered (all in feet), the slope angle (in degrees), and a flow condition — low, medium, or high.

Volume. The calculator multiplies length, width, and depth to get cubic feet, then divides by 27 to convert to cubic yards, the unit stone suppliers usually quote.

$\text{Volume (yd}^3\text{)} = \frac{\text{Length} \times \text{Width} \times \text{Depth}}{27}$

D50 stone size. Instead of asking for an exact water velocity, the calculator uses three flow bands, each tied to a base stone size:

That base size is then adjusted for the slope angle. A stone sitting on a slope has less friction holding it in place than one on flat ground, so steeper slopes need larger stones. The calculator applies a slope correction factor, K1:

$K_1 = \sqrt{1 - \frac{\sin^2(\theta)}{\sin^2(\phi)}}$

$D_{50} = \frac{\text{Base } D_{50}}{K_1}$

Here θ is the slope angle entered by the user, and φ is 40 degrees, the angle of repose used by the calculator — the steepest angle at which dumped rock naturally stays put. On flat ground (θ = 0°), K1 equals 1, so D50 equals the base size. As the slope angle climbs toward 40°, K1 shrinks toward zero and the required D50 grows very large. At 40° or beyond, the calculator returns "Infinity": no stone size, however large, will stay stable on a slope that steep, and the site needs a structural solution such as a concrete or gabion wall instead of loose rock. This slope correction follows the method in the U.S. Army Corps of Engineers manual EM 1110-2-1601 and the Natural Resources Conservation Service's National Engineering Handbook, Part 654, Technical Supplement 14C.

Rock size class. The calculator sorts the D50 result into one of five named classes:

Tonnage. The calculator converts volume to weight using a fixed placed density of 1.5 tons per cubic yard, the value used in FHWA's Hydraulic Engineering Circular 15. This density does not change with stone size — bigger rock has bigger gaps between pieces, so a cubic yard of large riprap and a cubic yard of small riprap weigh about the same once placed. (Field measurements vary from about 1.2 to 1.7 tons per cubic yard depending on gradation and how tightly the rock is packed; the calculator uses the single mid-range value of 1.5.)

$\text{Tonnage} = \text{Volume (yd}^3\text{)} \times 1.5$

Worked example

Consider a stream bank protection area 50 feet long, 20 feet wide, with a riprap depth of 2 feet, a 25° slope, and medium flow (5–10 ft/s).

Volume:

$\frac{50 \times 20 \times 2}{27} = \frac{2000}{27} \approx 74.1 \text{ yd}^3$

D50:

$K_1 = \sqrt{1 - \frac{\sin^2(25^\circ)}{\sin^2(40^\circ)}} \approx \sqrt{1 - 0.432} \approx 0.753$

$D_{50} = \frac{9}{0.753} \approx 11.9 \text{ inches}$

That falls in the 8–12 inch range, so the calculator reports Class III – Large Riprap.

Tonnage:

$74.1 \times 1.5 \approx 111.1 \text{ tons}$

For this project, the calculator would report roughly 11.9-inch D50 stone, 74.1 cubic yards, and 111.1 tons of rock.

Installation guidance

Alongside the numbers, the calculator lists installation notes that change with the inputs. Every result includes putting geotextile fabric under the riprap to stop soil from washing up through the gaps, and placing stones in a random, interlocking pattern rather than stacking them in neat rows. For slopes steeper than 30°, it recommends mechanical anchoring or terracing and building the slope from the bottom up so stones do not slide during construction. For high-flow sites, it adds a note about toe protection at the base of the slope. A general rule repeated across engineering guidance, and reflected in the calculator's notes, is that the riprap layer should be at least 1.5 times the D50 size thick, so that stones overlap rather than sitting exposed in a single layer.

Frequently asked questions

What is D50 in riprap sizing? D50 is the median stone size in a load of riprap: half the stones by weight are larger, half are smaller. Engineers specify D50 rather than the biggest stone because riprap performs as an interlocking mass, not as individual rocks.

What formula does this calculator use for D50? It starts from a base stone size tied to the flow condition (6 inches for low flow, 9 for medium, 12 for high), then divides that by a slope correction factor, K1 = √(1 − sin²θ / sin²40°), where θ is the slope angle. Steeper slopes produce a smaller K1 and therefore a larger required D50.

Why does the calculator show "Infinity" for D50? This happens when the slope angle is 40° or steeper, the angle of repose the calculator uses for dumped rock. At or above that angle, loose stone cannot stay in place on its own, regardless of size, so the site needs a structural retaining solution instead of riprap.

How does the calculator convert volume to tonnage? It multiplies the volume in cubic yards by a fixed placed density of 1.5 tons per cubic yard. This density is the same for every stone size in the calculator; it does not increase with larger D50 values.

Does the calculator apply a safety factor to its results? No. The volume, D50, and tonnage figures are the calculator's raw outputs with no built-in safety margin. Project designers commonly add their own margin on top of a base calculation to cover uncertainty in flow estimates and construction variation, but this calculator does not do that automatically.

What is the difference between riprap and rip rap? None. Both spellings refer to the same material: angular rock placed for erosion control. "Riprap," written as one word, is the spelling used in most engineering specifications and government publications.