How this instrument works
Vickers hardness measures how strongly a material resists a permanent dent from a diamond indenter pressed in under a known force. The indenter is a square-based pyramid ground to a precise 136° angle between opposite faces, so every test — soft aluminium or hardened tool steel — leaves a geometrically similar square mark whose size simply scales with how easily the material yields. Because the shape never changes, the entire hardness figure reduces to one ratio: how much force it took, divided by how much surface accepted that force.
That surface is not the flat square you would measure with calipers — it is the slanted pyramidal face actually in contact with the material, and converting the diagonal you see under a microscope into that slanted area brings in the indenter's angle through a sine term. Working through the geometry, the contact area comes out to d² ⁄ (2 sin 68°), where d is the mean of the two diagonals, so hardness — force over area — becomes HV = 2F sin(68°) ⁄ d², which collapses to the calculator's constant, 1.8544, because 2 sin(68°) equals that value to four decimal places. Vickers testing fixed the angle at 136° specifically so its readings would sit close to the older Brinell scale it was designed to extend.
The method needs a flat, polished surface and strains at either extreme of the load range: too light a force on a rough or coarse-grained surface leaves a diagonal too small and ragged to measure consistently, while pressing hard into a thin case-hardened layer or coating can dent clean through to the softer material underneath and return a falsely low reading. Standards specify a minimum indentation size and a minimum spacing from any edge or neighbouring indent for exactly this reason — a diagonal measurement can mean different things depending on how it was produced.
- Enter the Test force, kgf applied through the diamond indenter — commonly 1 to 30 kgf for standard macro-Vickers testing, lighter loads for thin or delicate parts.
- Under a calibrated microscope, measure both diagonals of the square indentation and average them; enter that figure as the Mean indentation diagonal, mm.
- Read the Vickers hardness number (HV) — conventionally reported as a bare figure, with the load appended as a suffix, for example 350 HV30.
- If the field returns an error, recheck the measurement: the instrument rejects a zero or negative diagonal, since a real indentation always leaves a measurable mark.
Worked example — 30 kgf load, 0.4 mm mean diagonal
A quality-control check on a hardened tool-steel insert: a 30 kgf load presses the diamond pyramid in, and the two diagonals of the resulting square measure out at a mean of 0.4 mm under the microscope. Substituting F = 30 and d = 0.4 into HV = 1.8544 · F ⁄ d² gives 1.8544 × 30 ⁄ 0.16, which comes out to exactly 347.7 — reported as 347.7 HV30, naming the load alongside the number.
That figure sits comfortably in the hardened-tool-steel band, well above the roughly 150 HV of annealed mild steel and below the 700-plus HV a fully hardened, tempered-martensite edge can reach. A softer material leaving a larger 0.8 mm diagonal under the same 30 kgf load would read only about 86.9 HV — the diagonal and the hardness move in opposite directions for a fixed load, since a bigger dent always means the material gave way more easily.
Questions
What does the constant 1.8544 in the formula represent?
It is twice the sine of 68°, the half-angle of the Vickers indenter's 136° diamond pyramid, folded into one number so the formula goes straight from load and diagonal to hardness. It is not a fitted or empirical constant — change the indenter's face angle and this number changes with it, because it comes directly from the geometry that turns a flat diagonal measurement into the slanted contact area the diamond actually pressed against.
Why does hardness rise when the diagonal shrinks?
Because hardness is force divided by contact area, and a smaller diagonal means a smaller indentation for the same push. A harder material resists the indenter more, so the diamond sinks in less and leaves a smaller square; a softer one gives way further and leaves a bigger one. Doubling the test force to 60 kgf at the same 0.4 mm diagonal doubles the computed hardness to 695.4 HV, since it took twice the force to make an equally small mark.
How is the mean diagonal actually measured?
An operator views the square indentation under a calibrated microscope, measures both diagonals separately, and averages the two. They rarely match exactly — surface roughness, slight indenter wear, or a test axis not quite perpendicular to the surface leaves one diagonal a little longer than the other — and averaging cancels most of that asymmetry rather than trusting either single measurement alone.
Why use Vickers instead of Brinell or Rockwell?
Because one diamond pyramid and one formula cover nearly the entire hardness range, from soft aluminium to hardened tool steel, on a single continuous scale — Brinell's ball flattens against very hard material, and Rockwell needs a different scale (B, C, and others) for different hardness bands. Vickers indents are also small enough to test thin coatings, case-hardened layers, and individual grains that a Brinell ball would span straight across.
Can a Vickers number be converted to Rockwell or Brinell?
Only approximately, through empirical conversion tables built from side-by-side testing on specific alloy families — there is no exact physical equation linking the scales, because the three tests measure geometrically different indentations. Standard conversion tables exist for this purpose; treat any converted figure as an estimate, not a substitute for testing directly on the scale you actually need.
Why does a torn or barrel-shaped indentation invalidate the reading?
Because the formula assumes a clean, sharp-cornered square whose diagonal can be measured to within about a micrometre; a torn, cracked, or barrel-shaped mark — common on rough, coarse-grained, or badly polished surfaces — no longer matches the geometry the 1.8544 constant assumes, so the resulting number overstates or understates the true hardness. Standards require a minimum indentation size and a flat, polished test surface for exactly this reason.