Grain Size Converter: Millimeters, Phi, and Wentworth Class

If you’ve spent any time doing sediment description or grain size analysis, you already know the annoyance. Field logs and sieve data usually come in millimeters, but the moment you’re doing anything with grain size distributions statistically, phi units take over, and flipping between the two by hand, especially when phi involves a negative log base 2, is exactly the kind of arithmetic that’s easy to get wrong at the end of a long day.

The calculator on this page converts freely between millimeters, microns, and phi, tells you the matching Wentworth class automatically, and includes a settling velocity estimate for anyone working with fine grained sediment.

Why Phi Units Exist At All

Grain sizes in nature span an enormous range, from boulders more than a meter across down to clay particles smaller than a thousandth of a millimeter. Working directly in millimeters across that whole range is awkward, since the numbers involved swing from the thousands down to fractions with several decimal places, and standard statistics don’t behave well on a scale like that.

The phi scale, introduced by Krumbein in the 1930s building on Wentworth’s original grain size classes, solves this by taking the negative base 2 logarithm of the grain diameter in millimeters. The formula is straightforward: phi equals negative log base 2 of the diameter in millimeters, or written the other way, diameter equals 2 raised to the power of negative phi.

The negative sign is what throws people off at first, but it exists for a good reason. Because of the negative sign and the log relationship, coarser grains get negative phi values and finer grains get positive phi values, and each whole step in phi represents the grain size doubling or halving. A grain of 1 mm sits at phi 0. A grain of 2 mm sits at phi negative 1. A grain of 0.5 mm sits at phi positive 1. Once that clicks, moving through the scale becomes intuitive, and it makes standard statistical methods, like calculating mean grain size or sorting from a distribution, actually well behaved.

The Wentworth Scale, Class by Class

The Wentworth scale (technically the Udden-Wentworth scale, since Udden proposed the original logarithmic grade scale and Wentworth extended and popularized it) breaks the full range of natural sediment sizes into named classes, each spanning exactly one phi unit through the sand and finer range, with broader steps for gravel sized material.

From coarsest to finest: boulder (larger than 256 mm), cobble (64 to 256 mm), pebble (4 to 64 mm), granule (2 to 4 mm), then the sand classes running from very coarse sand down to very fine sand between 1 mm and 0.0625 mm, then silt subdivided the same way from coarse to very fine silt between 0.0625 mm and 0.0039 mm, and finally clay for anything finer than 0.0039 mm.

It’s worth knowing that the sand, silt, and clay boundaries used here (0.0625 mm for sand/silt and 0.0039 mm for silt/clay) are the geological convention. Engineering soil classification systems, like the ones used in construction and geotechnical work, sometimes draw those same boundaries at slightly different values, most commonly using 0.075 mm as the sand/silt cutoff instead of 0.0625 mm. If you’re moving between a geology report and a geotechnical one, it’s worth double checking which convention is in play, since the class name alone doesn’t guarantee the exact same size range.

A Quick Example

Say you’ve sieved a sample and measured a grain at 0.18 mm. Converting to phi: negative log base 2 of 0.18 works out to about 2.47. That phi value falls in the range for fine sand (phi 2 to 3), so this grain gets classified as fine sand.

Going the other direction, say a lab report gives you a mean grain size of phi 6.2 for a sample. Converting back to millimeters: 2 raised to the power of negative 6.2 comes out to about 0.0136 mm, which falls into the fine silt range.

Why Settling Velocity Matters Alongside Grain Size

Grain size and settling velocity are closely linked, since how fast a particle sinks through still water depends heavily on its size, along with its density and the fluid it’s settling through. For fine grained sediment, roughly silt and clay sized material, Stokes’ Law gives a reasonably good estimate of settling velocity, based on the balance between gravity pulling the particle down and viscous drag from the fluid resisting that motion.

The settling velocity section on this page uses Stokes’ Law directly, and it’s genuinely useful for anyone thinking about how long suspended sediment takes to settle out in a quiet water column, or roughly how a lab based settling tube analysis should behave for a given grain size.

The catch is that Stokes’ Law assumes slow, smooth, laminar flow around the settling particle, which holds up well for small grains but breaks down as grains get larger and settle faster, since the flow around them becomes turbulent instead. Past roughly 0.1 to 0.2 mm, sand sized material starts settling faster than Stokes’ Law predicts, and a different, more complex formula is really needed for an accurate number. The calculator flags this automatically if your grain size is outside the range where the simple formula holds up well.

Common Mistakes

Forgetting the negative sign when converting mm to phi by hand, which flips coarse and fine grains in the wrong direction entirely.

Mixing up geological and engineering size class boundaries, especially around the sand/silt cutoff, when comparing reports from different disciplines.

Applying Stokes’ Law to sand sized or larger grains and treating the result as accurate, when the underlying assumption of laminar flow no longer holds at that size.

Rounding phi values too aggressively before converting back to millimeters, since phi is a logarithmic scale and small rounding errors get amplified once you exponentiate back to a linear size.

Who Uses This

Sedimentologists and geologists doing grain size analysis on core samples, outcrop samples, or sieve data.

Students learning the Wentworth scale and phi notation for the first time and wanting a fast way to check conversions.

Geotechnical engineers and lab technicians moving between geological grain size reporting and engineering soil classification.

Anyone working with sediment transport or deposition who needs a quick settling velocity estimate for fine grained material.

Try It Above

Enter a value in whichever unit you have, millimeters, microns, or phi, and get the other two along with the matching Wentworth class instantly. If you’re working with silt or clay sized material, the settling velocity section carries your grain size over automatically so you can get a quick estimate without re-entering it.

Related Calculators and Reference

• Sieve Analysis and Gradation Test, for the test that produces the distribution you are converting.
• USCS Soil Classification Tool, to turn the gradation into a classification.
• Soil Description Generator, to write the description once the class is settled.
• Void Ratio, Porosity and Unit Weight Converter, for the density terms that go alongside the grading.
• Mesh to Micron Converter, for the sieve number to opening step behind a sieve stack.
• ASTM D2487, the classification standard these size boundaries feed.