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?

The average grain diameter in mm at 100× is d = 1 / sqrt(2^(G+3)). This is equivalent to N_A = 2^(G−1) grains per square inch at 100× magnification (= 2^(G+3) grains per mm²). The inverse formula is G = (2 × log2(1/d) − 3), where d is in mm.

What is the valid range of grain size numbers?

ASTM E112 formally covers G 00 (−2) through G 14. Negative grain size numbers represent extremely coarse grains (single-crystal or cast structures). Grain size numbers above 14 describe ultrafine or nanocrystalline materials.

How does grain diameter relate to grain area?

ASTM E112 models each grain as a circle. The average cross-sectional area A = π × (d/2)² where d is the mean lineal intercept diameter. Grains per unit area N_A = 1 / A.

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 tool for non-metallic materials?

Yes. The ASTM E112 formula is mathematically applicable to any polycrystalline material (ceramics, ice, geological minerals). However, ASTM E112 was written for metals, so supplementary standards (e.g., ASTM E1181 for duplex grain sizes) may apply to non-metallic microstructures.

Grain Size Number

Name: Grain Size Number
Availability: InStock
Author: Nham Vu

Convert an ASTM E112 grain size number to average grain diameter and area, or reverse-calculate the grain size number from a measured diameter.

Input

Conversion Direction

Grain Size Number (G)

Typical range: −3 to 14 (ASTM E112)

Output Diameter Unit

Results

Enter a value and click Calculate

ASTM E112 Reference Table

G	Diameter (µm)	Area (µm²)	Grains / mm²

Summary

Convert an ASTM E112 grain size number to average grain diameter and area, or reverse-calculate the grain size number from a measured diameter.

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 applies the ASTM E112 formula: d = 1 / sqrt(2^(G+3)) in mm at 100× magnification.
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: 2026-06-10 · Reviewed by Nham Vu