Vickers Hardness Number Interactive Calculator

If you’re dealing with heat-treated parts, case depths, or surface coatings, picking the correct hardness test method makes a big difference. Vickers is unique in that you can cover a wide hardness range on one scale without swapping test methods. The calculator here lets you solve for Vickers Hardness (HV), diagonal size, or applied force, all using the standard geometry for the square pyramidal indenter. It’s handy for everything from verifying steel hardening and aerospace specs, to measuring thin coatings. You’ll find the main HV formula, a typical inspection example, an explanation of the indentation geometry, and a detailed FAQ below.

What is Vickers Hardness Number?

Vickers Hardness Number (HV) tells you how much a material resists permanent indentation from a diamond pyramid pushed in at a known load. Harder materials leave smaller dents, so a higher HV number means a harder surface.

Simple Explanation

If you press a diamond-tipped pyramid into a material and then measure the size of the impression, you’ll get a sense of its hardness. A shallow, small mark signals a harder material; a bigger one points to something softer. The Vickers number just gives you a way to put this into a calculated value—smaller impression, higher HV; bigger impression, lower HV.

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Visual Diagram: Vickers Indentation Geometry

Vickers Hardness Number Calculator

How to Use This Calculator

1. Select your Calculation Mode from the dropdown — choose whether you want to calculate HV, find the diagonal, determine the required force, convert units, compare two tests, or calculate indentation surface area.
2. Enter the Applied Force in kgf and/or the Average Diagonal in μm as required by the selected mode.
3. If your mode requires it, enter the Vickers Hardness (HV) or a second set of test values for comparison.
4. Click Calculate to see your result.

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Vickers Hardness Equations

The equation below gives you Vickers Hardness Number using the force and measured diagonal.

Here’s the formula to get the surface area of the indentation.

This conversion is for switching between kilograms-force and Newtons.

This formula gives the average contact pressure under the pyramid.

Simple Example

Inputs: Applied force F = 5 kgf, average diagonal d = 142.5 μm (= 0.1425 mm)
HV = 1.8544 × 5 / (0.1425)²
HV = 9.272 / 0.020306 = 456.6 HV
Force in Newtons: 5 × 9.80665 = 49.03 N

Theory & Practical Applications of Vickers Hardness Testing

Fundamental Principles of Vickers Indentation

The Vickers test uses a diamond pyramid with a 136° angle. This shape means that no matter what load you use, you still get the same proportional indentation. That’s different from Brinell, where the ball shape changes the force-to-area ratio depending on the load. The constant 1.8544 comes straight from the pyramid geometry—2sin(68°), since 68° is the half-angle measured from the axis. Because the scaling is consistent, you can apply this method from very soft metals (~50 HV) up to over 1500 HV for hard carbides without needing several test scales or indenters.

One clear upside: this “load independence” lets you test thin surface layers, like a carburized case on a gear, using microhardness loads (HV0.1) in one part and macro loads (HV30) in another—all on the same scale. As you scale up the force and the impression, the actual mean stress under the indenter stays the same. If you want a rough idea: 500 HV = roughly 4.9 GPa pressure—close to the yield strength you’ll see in hardened steels.

Optical Measurement Precision and Error Sources

Measuring diagonals accurately is the main challenge in Vickers testing. Since HV depends on the square of the diagonal, even a small measurement error has a big impact—a 2% error in diagonal gives about 4% error in HV. Automated digital systems are repeatable if you have sharp, clean indents, but rough surfaces, pile-up (material pushed up around the impression), and sink-in (edges curve inward because of elastic recovery) all make things trickier. For comparison, ISO 6507 calls for dumping results if diagonal difference is over 5% for d > 0.2 mm.

Surface prep is critical. For microhardness, roughness should be under 0.05 μm, which means fine polishing with diamond or colloidal silica. With coarser surfaces, some of the load gets taken by peaks, and you’ll read a falsely high hardness. For very hard steels and ceramics, even the indenter tip can compress elastically by 1–2 μm, and you’ll need to check your test setup against a known reference block. If you get cracks, big pile-up, or oddly shaped impressions at high HV values (above about 1200), these are real material or setup effects, not device problems.

Industrial Application in Heat Treatment Verification

In aerospace or anywhere tight specs matter (think surface or through-hardening windows of 160–190 HV on 7075-T6 aluminum or 345–390 HV on Ti-6Al-4V), Vickers is used for both spot checks and hardness profiles. It’s also common to use it for case depth or gradient mapping, and to estimate tensile strength (for ferritic steels, σ_UTS ≈ 3.3 × HV is a common rough estimate). Just remember: this conversion does not hold in all metals, especially if strain hardening is significant or the structure is not single phase.

Austenitic stainless tends to harden as you indent it—expect 15–20% higher HV than its tensile strength would predict. Cast irons, with graphite flakes, will give a lower HV number compared to the same tensile strength in steels. On curved surfaces (like crank journals), the impression may go elliptical and inflate your numbers if the part radius gets close to the indentation size—keep the surface radius above 2.5× the indentation diagonal for an accurate reading, or switch to lighter loads and microhardness if required. Space your indents: 3d apart (center to center) and at least 2.5d from any edge or you’ll get higher readings from overlapping plastic zones.

Worked Example: Quality Control of Carburized Steel Component

Scenario: You’re making carburized 8620 gears and need a surface hardness of 58–63 HRC (660–810 HV) with a typical case of 0.9–1.2 mm. Use a 1 kgf microhardness test (HV1) at 0.1 mm steps. At 0.15 mm depth, diagonal is 118.6 μm. Let’s check if that spot meets spec, find the geometry, and look at proper spacing.

Step 1: Calculate Vickers Hardness

Diagonal in mm: d = 118.6 μm = 0.1186 mm

Plug into the Vickers formula (F = 1 kgf):

HV = 1.8544 × F / d² = 1.8544 × 1 / (0.1186)² = 1.8544 / 0.01407 = 131.7 HV

Result: HV1 = 131.7 (way below target)

Step 2: Calculate Indentation Surface Area

A_s = d² / 1.8544 = (0.1186)² / 1.8544 = 0.01407 / 1.8544 = 0.007587 mm²

In μm²: A_s = 7,587 μm²

Step 3: Estimate Indentation Depth

h ≈ d/7 for Vickers (136°) pyramids:

h = 118.6 / 7 = 16.9 μm

That’s much less than the 0.15 mm measurement depth, so test location is fine.

Step 4: Calculate Mean Contact Pressure

Force: 1 kgf × 9.80665 = 9.807 N

P_m = F / A_s = 9.807 N / (7,587 × 10⁻¹² m²) = 1.29 GPa

Step 5: Determine Test Spacing Requirements

Minimum spacing per ISO 6507: 3 × d center-to-center

Minimum spacing = 3 × 118.6 μm = 355.8 μm ≈ 0.36 mm

The 0.1 mm planned spacing is too close—your plastic zones will overlap and readings won’t be independent.

To fit closer spacing, reduce load: Use HV0.5 (smaller diagonal ~84 μm) for min spacing of 252 μm, or HV0.3 for tighter intervals if needed.

Analysis: 131.7 HV at 0.15 mm is way under spec for a carburized case. Most likely you’ve gone past the case or the process failed. Core hardness should be 250–350 HV for 8620, with a surface above 660 HV. Try again closer to the surface and check your test spacing and loads are correct for the case thickness and required intervals.

Advanced Considerations: Load-Dependent Behavior and Indentation Size Effect

Even though the Vickers test is supposed to be load-independent, most metals (especially if cold-worked) show the “Indentation Size Effect” at light loads (under 200 gf). You’ll get artificially higher hardness with lighter loads—10%–30% higher at 10 gf compared to 1 kgf—because of higher dislocation density under tiny indents. When the indent becomes similar to the grain size, orientation effects cause scatter; for decent statistics you’ll need 10–15 indents on large-grain metal. With nanoindentation, you’re right in the grain, not the bulk material.

At tiny loads, a lot of the indentation is elastic and springs back, so your diagonal might not represent the maximum load state. Pile-up doesn’t develop properly, which can lead to underestimating area and exaggerating the HV value. For comparison and spec work, keep loads above HV1. If you have to use very low loads (HV0.05 or less), just treat the number as a comparative index, not a true quantitative hardness.

Frequently Asked Questions

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