Enter the trials of a compaction test: the water content of each and the mass of the mold with the compacted soil. The calculator works out each trial’s dry density, draws the compaction curve under the 100 % saturation line, and gives the maximum dry density and the optimum moisture content. It covers the standard Proctor (ASTM D698) and the modified one (ASTM D1557), and it’s free and needs no account.

Calculator · ASTM D698 · D1557

Compaction trials

One trial per water content, in increasing order. The mass is the mold's with its base and the compacted soil.

Trial	Water content(%)	Mold with its base and the soil(kg)
#1
#2
#3
#4
#5
#6
#7
#8

The standard asks for at least four trials, two on each side of the optimum. If the optimum falls at the edge, that side is short of trials.

Mold

The volume comes from its size, and it's the denominator of every density. A 4-inch mold holds about 940 cm³; the calculation takes what you measure, not a catalog value.

Mass of the mold with its base

Inner diameter

Height

Soil and water

The specific gravity draws the 100 % saturation line, the test's physical limit. The water's density is the one at the laboratory's temperature.

Specific gravity · Gs

Water density

kg/m³

Compaction curve

Trials
100 % saturation

8 compaction trials, 4 before the optimum and 3 after. The densest trial is the one at 10.0 % water content, with 1898 kg/m³ of dry density: that's the test's optimum and maximum density

The test's result

Quantity	Value
Mold volume(D/2)² · π · H	919.8cm³
Optimum water content · woptthe densest trial measured	10.0%
Maximum dry density · γd,maxthe same trial, without the water	1898kg/m³

This calculator is offered for information and technical support. It doesn't replace professional judgment or the reviews due, and its use is the user's responsibility.

How it calculates

The two tests compact with different energy, but their calculation is the same. The mold’s volume comes from its measured inner diameter $D$ and height $H$ , and each trial’s density from the mass of soil in it:

V = \pi \left(\frac{D}{2}\right)^2 H, \qquad \rho = \frac{M_t - M_m}{V}, \qquad \rho_d = \frac{\rho}{1 + w}

$M_t$ is the mold with its base and the compacted soil, $M_m$ the mold with its base, and $w$ the trial’s water content. Beside the curve, the calculator draws the zero-air-voids line: the dry density the soil would have at each water content if water filled all its voids.

\rho_{d,\text{sat}} = \frac{G_s\,\rho_w}{1 + w\,G_s}

The maximum dry density and the optimum moisture content are those of the densest trial, with no curve fitted between the points, so trials at close water contents pin the optimum down better. The calculator warns about fewer than four trials or fewer than two on each side of the optimum, water contents out of increasing order, a trial above the saturation line, which can’t happen, and an optimum at the driest or the wettest trial, which means the test needs points beyond it.

The full procedure, equipment and report are in the Academy lesson: Proctor compaction test.

How to use it

Under Compaction trials, enter each trial’s water content, in %, and the mass of the mold with its base and the compacted soil, in kg, from the driest trial to the wettest. Add a trial and Remove the last change how many there are.
Under Mold, enter the mass of the mold with its base, and its inner diameter and height in cm. A 4-inch mold holds about 940 cm³, but the calculation takes the size you measure.
Under Soil and water, enter the specific gravity of the soil, which draws the saturation line, and the density of water at the lab’s temperature, in kg/m³.
Read the compaction curve with the 100 % saturation line. The headline figure is the optimum moisture content, and the table gives the mold’s volume and the maximum dry density.

Restore the example brings back the eight trials of the worked example. If you don’t have $G_s$ , the specific gravity calculator works it out from a pycnometer test.

Frequently asked questions

What is a Proctor test used for?

It finds the densest state a soil reaches under a set compaction energy, and the water content that gets it there. Earthwork specifications use those two numbers as the target: the fill is placed near the optimum moisture content and compacted to a share of the maximum dry density.

What does 95 % Proctor mean?

That the dry density measured in the field is at least 95 % of the maximum dry density from the laboratory test the specification names, standard or modified. That share is called the relative compaction.

What is the difference between standard and modified Proctor?

The compaction energy. The standard test, ASTM D698, drops a 24.5 N (5.5 lbf) rammer 305 mm (12 in) onto three layers, for about 600 kN·m/m³. The modified test, ASTM D1557, drops a 44.5 N (10 lbf) rammer 457 mm (18 in) onto five layers, for about 2,700 kN·m/m³. More energy gives a higher maximum dry density at a lower optimum moisture content.

What is the zero-air-voids line?

The dry density the soil would reach at each water content with no air left in its voids: $\rho_d = G_s\,\rho_w/(1 + w\,G_s)$ . No compacted point can lie above it, and on the wet side of the optimum the compaction curve runs close to it and roughly parallel.

Proctor test calculator: maximum dry density and OMC