Cu and Cc: what the two gradation coefficients actually tell you

Updated: 2026-08-04 · ISKRIT

Two numbers describe the shape of a grain size curve. Cu says how wide the range of sizes is, Cc says whether the curve is smooth across that range. Both are needed, and each alone is misleading.

Definitions

Cu = d60 / d10 is the coefficient of uniformity. It is the ratio of the size that 60 % of the mass is finer than to the size that 10 % is finer than. A uniform sand from a dune sits near 2. A glacial till can pass 100.

Cc = d30² / (d10 · d60) is the coefficient of curvature. It compares the actual d30 with the value a smooth log-linear curve would have between d10 and d60. Values near 1 mean smooth, values below 1 mean the middle sizes are under-represented, values above 3 mean they dominate.

The thresholds

Sand carries the higher uniformity threshold because a narrow gravel band still contains a broad absolute range of particle sizes, while a narrow sand band does not.

Why Cu alone fails

A gap-graded soil, coarse gravel poured onto fine sand with nothing in between, has an enormous Cu. Reading Cu alone would call it well graded, and it compacts badly, segregates during placement and gives an unreliable density. Cc catches exactly this case: with the middle sizes missing, d30 sits close to d10 and Cc drops well below 1.

The reverse failure is rarer but real. A soil with a pronounced middle bulge gives Cc above 3, meaning the curve is not smooth either, just bulged the other way.

A practical caution about d10

Cu and Cc both divide by d10, which is the least reliable point on most curves. It usually falls near or below the finest sieve, so it comes from extrapolation or from a hydrometer test with its own uncertainty. A 20 % error in d10 propagates straight into a 20 % error in Cu. When d10 lies below the finest sieve actually used, the honest report says the coefficients are indicative.

The coefficients are computed with the characteristic diameters in the grain size analysis tool.