What is the ASTM E112 grain size number?

ASTM E112 defines G by N = 2^(G−1), where N is the number of grains per square inch on an image at 100× magnification. Higher G means finer grains. G 5 corresponds to about 248 grains/mm² (63.5 µm average diameter) and G 10 to about 7,940 grains/mm² (11.2 µm).

How do I calculate G from the mean lineal intercept?

Use G = −6.643856 × log10(ℓ̄) − 3.288 with ℓ̄ in millimetres at 1×. Example: 1,000 µm of test line on the specimen (100 mm at 100×) crossing 50 grains gives ℓ̄ = 0.02 mm, so G = −6.643856 × log10(0.02) − 3.288 = 8.00.

How do I calculate G with the planimetric (Jeffries) method?

Count the grains completely inside a known test area and those cut by its boundary. N_A = (M² ÷ A) × (N_inside + N_intercepted ÷ 2), with A the test area on the image in mm². Then G = 3.321928 × log10(N_A) − 2.954. Example: a 5,000 mm² circle at 100× with 40 grains inside and 20 intercepted gives N_A = 2 × 50 = 100 grains/mm² and G = 3.69.

How do I convert a grain count made at another magnification?

The definition uses 100×. A count of n grains per in² at magnification M equals n × (M ÷ 100)² grains per in² at 100×. For example 64 grains/in² at 200× is 256 at 100×, which gives G = 1 + log2(256) = 9.

What is the difference between average diameter and mean intercept?

The average diameter d̄ = 1/√N_A is the side of a square with the mean grain area. The mean lineal intercept ℓ̄ is the average chord length a random line cuts through grains. For the same G, ℓ̄ is about 0.89 × d̄ in E112 (for G 5: ℓ̄ = 56.6 µm, d̄ = 63.5 µm), so do not mix the two when converting to G.

How does ASTM E112 G compare with ISO 643?

ISO 643 defines its index by m = 8 × 2^G grains/mm², whereas ASTM gives 7.75 × 2^G grains/mm². The ISO number is therefore about 0.046 lower than the ASTM number for the same structure, which is negligible in practice.

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 linear size by a factor of √2 (≈ 0.707).

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

No. ASTM E112 also specifies specimen preparation, etching, the number of fields, confidence limits and reporting. This calculator applies the conversion equations to measurements you already have.

Grain Size Number

Enter a grain size number G, an average diameter, a mean lineal intercept, or raw intercept / planimetric counts with the magnification, and get the ASTM E112 G, grains per mm², grains per in² at 100×, mean grain area, average diameter, mean intercept length and the approximate ISO 643 index.

Method scope: ASTM E112 covers planar average grain size and does not set material acceptance limits. Results convert measurements; they are not a full E112 test report.

Input

I have…

Grain size number G

Output length unit

Results

ASTM G

ISO 643 G (≈)

Average diameter d̄ = √Ā
Mean lineal intercept ℓ̄
Mean grain area Ā
Grains per mm² (N_A at 1×)
Grains per in² at 100×
Intercepts per mm (N_L)

Coarse (G 1)Fine (G 14)

ASTM E112 grain size relationships

Uniform, randomly oriented equiaxed grains. N_A at 1×; d̄ = 1/√N_A; ℓ̄ from G = −6.643856 log10(ℓ̄) − 3.288.

G	Grains/in² at 100×	Grains/mm²	Ā (µm²)	d̄ (µm)	ℓ̄ (µm)	N_L (mm⁻¹)
0	0.50	7.75	129,032	359.2	320.0	3.13
0.5	0.71	11.0	91,239	302.1	269.1	3.72
1	1.00	15.5	64,516	254.0	226.3	4.42
1.5	1.41	21.9	45,620	213.6	190.3	5.26
2	2.00	31.0	32,258	179.6	160.0	6.25
2.5	2.83	43.8	22,810	151.0	134.5	7.43
3	4.00	62.0	16,129	127.0	113.1	8.84
3.5	5.66	87.7	11,405	106.8	95.1	10.5
4	8.00	124	8,065	89.8	80.0	12.5
4.5	11.3	175	5,702	75.5	67.3	14.9
5	16.0	248	4,032	63.5	56.6	17.7
5.5	22.6	351	2,851	53.4	47.6	21.0
6	32.0	496	2,016	44.9	40.0	25.0
6.5	45.3	701	1,426	37.8	33.6	29.7
7	64.0	992	1,008	31.8	28.3	35.4
7.5	90.5	1,403	713	26.7	23.8	42.0
8	128	1,984	504	22.5	20.0	50.0
8.5	181	2,806	356	18.9	16.8	59.5
9	256	3,968	252	15.9	14.1	70.7
9.5	362	5,612	178	13.3	11.9	84.1
10	512	7,936	126	11.2	10.0	100
10.5	724	11,223	89.1	9.4	8.4	119
11	1,024	15,872	63.0	7.9	7.1	141
11.5	1,448	22,446	44.6	6.7	5.9	168
12	2,048	31,744	31.5	5.6	5.0	200
12.5	2,896	44,893	22.3	4.7	4.2	238
13	4,096	63,488	15.8	4.0	3.5	283
13.5	5,793	89,786	11.1	3.3	3.0	336
14	8,192	126,976	7.88	2.8	2.5	400

Equations

N(100×, per in²) = 2^(G−1) · N_A = N × (100/25.4)² = 15.50 N

G = 3.321928 log10(N_A) − 2.954 · G = −6.643856 log10(ℓ̄ mm) − 3.288

Heyn: N_L = N·M / L, ℓ̄ = 1/N_L · Jeffries: N_A = (M²/A)(N_inside + ½ N_intercepted)

Worked example (intercept): 100 mm of test line at 100× crosses 50 grains → N_L = 50 × 100 / 100 = 50 mm⁻¹, ℓ̄ = 0.020 mm = 20 µm → G = −6.643856 × log10(0.020) − 3.288 = 8.00.

Summary

ASTM grain size number G is a logarithmic index: N = 2^(G−1) grains per square inch on an image at 100×, so each +1 in G doubles the grain count and makes grains finer. In metric terms G = 3.321928 log10(N_A) − 2.954 with N_A in grains/mm² at 1×, and for the intercept method G = −6.643856 log10(ℓ̄) − 3.288 with the mean lineal intercept ℓ̄ in mm. The calculator applies these ASTM E112 relationships, converts counts made at any magnification, and lists the average grain area, the area-derived diameter d̄ = 1/√N_A, the intercept length and the approximate ISO 643 number. It converts measurements; specimen preparation, the number of fields and the statistics required for an E112 test report are up to the laboratory.

How it works

Choose what you have: a G number, an average diameter, a mean intercept length, intercept counts or planimetric counts.
For intercept counts (Heyn/Abrams) enter the number of intercepts or boundary intersections, the total test-line length on the image and the magnification: N_L = N × M ÷ L, ℓ̄ = 1 ÷ N_L.
For planimetric counts (Jeffries) enter grains completely inside the test area, grains cut by its boundary, the test area on the image and the magnification: N_A = (M² ÷ A) × (N_inside + ½ N_intercepted).
The calculator converts to G with the ASTM E112 equations and back to every other measure.
Compare with the static table of G 0–14, which lists the same quantities in half-number steps.

Use cases

Verify acceptance criteria for steel, aluminum, or titanium grain size specifications.
Turn raw Heyn intercept or Jeffries planimetric counts into an ASTM G number.
Convert between micron diameters reported in research papers and ASTM G numbers.
Convert counts made at 200×, 500× or 1000× to the 100× basis of the definition.
Quality-control incoming raw material mill certificates.
Education: illustrate the exponential relationship between G and grain size.

Frequently Asked Questions

Last updated: 2026-10-10 · Reviewed by Nham Vu