Enter the hydrometer readings of a soil suspension and the time of each. The calculator turns every reading into a particle diameter, by Stokes’ law, and a percent finer, and draws the grain size curve of the silt and clay that sieving can’t sort. It takes the 151H and the 152H hydrometers and follows ASTM D7928. It’s free and needs no account.

Calculator · ASTM D7928

Hydrometer used

The two read differently and each has its own formulas. The 151H reads the suspension's specific gravity, from 0.995 to 1.038: write it as read, like 1.0226. The 152H reads grams of soil per liter, from −5 to 60: write it in g/L, like 36.5.

Changing the hydrometer changes the example: they aren't the same numbers. The 151H's effective depth comes from its calibration: the two marks below, their distances and the meniscus correction (ASTM D7928).

Hydrometer readings

Each reading as its scale gives it, at the top of the meniscus: a specific gravity, like 1.0226. The water-with-dispersant reading is among the parameters, below: it's what's subtracted to know how much material is still in suspension.

Reading	Time(min)	Hydrometer reading
#1
#2
#3
#4
#5
#6
#7
#8
#9

The first nine rows are the times the standard asks for. You can add your own: 2880 min, or others your test recorded.

The hydrometer's constants

From the instrument's calibration: the two readings at the meniscus marks, their distances to the bottom and the meniscus correction. With them each reading is corrected into its effective depth.

Upper meniscus · r₁

Lower meniscus · r₂

Upper one's depth · H_r1

Lower one's depth · H_r2

Meniscus correction

Suspension

The water-with-dispersant reading is the zero: what's above it is the material in suspension. The viscosity and the density are the water's at the test's temperature.

Reading with dispersant only

As a specific gravity, like the readings: 1.0022.

Water viscosity

Water density

g/cm³

Specific gravity · Gs

Soil dry mass

Suspension volume

cm³

Grading curve

9 readings cover 0.0467 to 0.0014 mm; 35.1 % of the soil is still in suspension at the end, the material finer than sieving can measure

Each reading and its equivalent diameter

Quantity	Value
1 mindepth 10.70 cm	0.0467mm
2 mindepth 10.89 cm	0.0334mm
4 mindepth 11.09 cm	0.0238mm
8 mindepth 11.37 cm	0.0170mm
15 mindepth 11.65 cm	0.0126mm
30 mindepth 11.93 cm	0.0090mm
60 mindepth 12.24 cm	0.0065mm
240 mindepth 13.00 cm	0.0033mm
1440 mindepth 13.76 cm	0.0014mm

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

Each reading gives a depth, a diameter and a percent finer, and the depth and the percent depend on the hydrometer.

The effective depth is the distance from the surface of the suspension to the hydrometer’s center of buoyancy. The 151H’s comes from its calibration: the readings $r_1$ and $r_2$ at two marks, their depths $H_{r1}$ and $H_{r2}$ , and the meniscus correction $C_m$ , since every reading is taken at the top of the meniscus. The 152H’s comes from the geometry of its scale, as the former ASTM D422 gives it, in cm:

H = H_{r2} + \frac{H_{r1} - H_{r2}}{r_2 - r_1}\,(r_2 - r_m - C_m) \qquad \text{(151H)}

L = 16.295 - 0.164\,R \qquad \text{(152H)}

The diameter comes from Stokes’ law: a small sphere settles through still water at a speed that grows with the square of its diameter, so after a time $t$ the largest particles left at the depth $H$ have the diameter

D = \sqrt{\frac{30\,\eta}{g\,(G_s - G_w)} \cdot \frac{H}{t}}

with $D$ in mm, the water’s viscosity $\eta$ in poises (the field takes centipoises), $g$ = 980 cm/s², $H$ in cm and $t$ in minutes. For the 152H, $G_w$ is the density of water you enter; for the 151H it’s 1, with $g$ = 981 cm/s².

The percent finer compares each reading, $r_m$ , with the reading of water and dispersant without soil, $r_d$ , which is the zero. The 151H reads specific gravity and the 152H grams of soil per litre, so each has its own equation in ASTM D7928:

N = \frac{G_s}{G_s - 1} \cdot \frac{V}{M_d}\,\rho_w\,(r_m - r_d) \times 100 \qquad \text{(151H)}

N = \frac{a\,(R_m - R_d)}{M_d} \cdot \frac{V}{1000} \times 100, \qquad a = \frac{1.65}{2.65} \cdot \frac{G_s}{G_s - 1} \qquad \text{(152H)}

$V$ is the volume of the suspension in cm³ and $M_d$ the dry mass of soil in it. The 152H’s scale assumes $G_s$ = 2.65, and $a$ corrects for any other value. The calculator warns when a diameter falls outside 0.001 to 0.063 mm, the range where it takes the method to hold; when the percent finer rises with time, a sign that the soil flocculated; and when there’s more dry soil than the hydrometer can take.

The full procedure, equipment and report are in the Academy lesson: Hydrometer analysis of soil.

How to use it

Pick the hydrometer you used: the 151H reads the suspension’s specific gravity, written as read (1.0226), and the 152H grams of soil per litre. Each one loads its own example.
Enter each reading and its time, in minutes. The first nine rows are the times the standard asks for, from 1 to 1440 minutes, and Add a reading takes later ones.
For the 151H, enter its calibration: the readings at the two marks, their depths and the meniscus correction. The 152H doesn’t need them.
Describe the suspension: the reading with dispersant only, the viscosity and density of water at the test’s temperature, $G_s$ , the soil’s dry mass and the volume.
Read the curve of percent finer against diameter, and each reading’s depth and diameter in the table. The headline figure is the share of soil still in suspension at the last reading.

Restore the example brings back the example of the hydrometer you picked. The coarser part of the curve, above 0.075 mm, comes from the sieve analysis calculator.

Frequently asked questions

What is a hydrometer analysis used for?

It measures the grain size distribution of the fines, the silt and clay that pass the No. 200 sieve (0.075 mm) and are too small to sieve. Joined to a sieve analysis, it completes the curve of a soil and shows how much of it is clay-sized.

What is the difference between the 151H and the 152H hydrometers?

Both are standard soil hydrometers, specified in ASTM E100. The 151H reads the specific gravity of the suspension; the 152H reads grams of soil per litre and assumes $G_s$ = 2.65. Each has its own depth and percent finer equations, which is why the calculator asks which one you used.

What is Stokes’ law?

It gives the speed at which a small sphere settles through a still fluid: $v = (\rho_s - \rho_w)\,g\,D^2/(18\,\eta)$ . Since the speed grows with the square of the diameter, the coarse particles leave the top of the cylinder first. Soil particles aren’t spheres, so the diameter the test gives is an equivalent one.

Why subtract the reading of water and dispersant?

The dispersant, usually sodium hexametaphosphate, keeps clay particles from clumping, and it also makes the water denser. A cylinder with the same dose and no soil gives the reading that counts as zero, so only what’s above it is soil in suspension.

Soil hydrometer analysis calculator (151H and 152H)