What is the ASTM E112 grain size number?

ASTM E112 defines a logarithmic grain size number G where the number of grains per square inch at 100× magnification equals 2^(G−1). Higher G means finer grains. Typical engineering alloys range from G 5 (coarse, ~64 µm) to G 10 (very fine, ~11 µm).

What formula is used?

ASTM E112 defines N = 2^(G−1) grains per square inch on a 100× image. Converting the image area to specimen area gives N_A = 2^(G−1) × (100/25.4)² grains/mm². This calculator reports the nominal planar diameter d = sqrt(1/N_A); the inverse is G = 1 + 2 log2(0.254/d), with d in mm.

What range does this calculator accept?

The calculator accepts G from −3 through 20 for numerical conversion. That input range is a calculator boundary, not a claim that every value is covered by a particular ASTM E112 edition or suitable for every microstructure.

How does grain diameter relate to grain area?

The mean planar grain area is A = 1/N_A. The displayed nominal diameter is sqrt(A), an area-derived size rather than an assumption that every grain is a circle.

Why does the number of grains double for each unit increase in G?

The grain count per unit area is proportional to 2^(G−1), so each +1 step in G exactly doubles the number of grains, halves the area per grain, and reduces the diameter by a factor of √2 (≈ 0.707).

Can I use this result as an ASTM E112 test report?

No. ASTM E112 includes comparison, planimetric and intercept procedures and addresses planar average grain size. This converter only transforms an already established G value or area-derived linear size; specimen preparation, calibration, counting and method reporting still matter.

Grain Size Number

Convert ASTM grain size number G to grains/mm², mean planar area and an area-derived linear size, or calculate G from that linear size.

Method scope: ASTM E112 covers planar average grain size and does not establish material acceptance limits. The displayed linear size is √(mean planar area), not a measurement of every grain or a 3D diameter.

Input

Conversion Direction

Grain Size Number (G)

Calculator range: −3 to 20; confirm the applicable standard edition and method.

Output Diameter Unit

Results

Enter a value and click Calculate

ASTM E112 Reference Table

G	√Area (µm)	Area (µm²)	Grains / mm²

Summary

ASTM grain size number G is a logarithmic index: the number of grains per unit area doubles for each unit increase in G. This calculator converts the count relationship into mean planar area and sqrt(area), an area-derived linear size. It does not replace a comparison, planimetric or intercept measurement under ASTM E112.

How it works

Choose whether to convert from grain size number G or from a measured diameter.
Enter the grain size number (typically 1–14) or the average grain diameter.
Select your preferred output unit (µm, mm, or inches).
The calculator derives mean planar grain area from N = 2^(G−1) grains/in² on a 100× image, then reports L = sqrt(1/N_A).
Results show average grain diameter, average grain cross-sectional area, and grains per mm².

Use cases

Verify acceptance criteria for steel, aluminum, or titanium grain size specifications.
Convert ASTM grain size numbers when comparing international material standards.
Back-calculate G from metallographic image analysis measurements.
Estimate grain boundary area per unit volume for diffusion or creep studies.
Quality-control incoming raw material mill certificates.
Support failure analysis reports requiring grain size characterization.
Education: illustrate the exponential relationship between G and grain diameter.
Convert between micron diameters reported in research papers and ASTM G numbers.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu