Mohs Hardness Relative Scaling Calculator

Formula first

Overview

This empirical formula provides a mathematical approximation for converting the qualitative Mohs scale of mineral hardness into a quantitative absolute value. It illustrates that mineral hardness increases exponentially rather than linearly as the scale rank progresses.

Symbols

Variables

$H_{abs}$ = Approx Absolute Hardness, M = Mohs Scale Rank

Apply it well

When To Use

When to use: Apply this formula when you need to estimate relative quantitative hardness from a qualitative Mohs rank. It is useful for material science comparisons where precise laboratory testing like Vickers or Knoop is unavailable.

Why it matters: The Mohs scale is not linear; for example, the hardness gap between Corundum (9) and Diamond (10) is much larger than between Talc (1) and Gypsum (2). This formula helps engineers understand the exponential energy and wear requirements for processing harder minerals.

Avoid these traps

Common Mistakes

• Assuming Mohs 8 is 'twice as hard' as Mohs 4. It's an ordinal rank, not a linear scale.
• Convert units and scales before substituting, especially percentages, time units, or powers of ten.
• Interpret the answer with its unit and context; a percentage, rate, ratio, and physical quantity do not mean the same thing.

One free problem

Practice Problem

Quartz has a Mohs hardness of 7. Using the relative scaling formula, calculate its approximate absolute hardness (HABS).

Solve for: HABS

Hint: Divide the Mohs rank by 2 and then use that result as the exponent for the base 2.

The full worked solution stays in the interactive walkthrough.

Keep going

Related Formulas

References

Sources

1. Britannica: Mohs scale
2. Wikipedia: Mohs scale of mineral hardness
3. Klein & Hurlbut: Manual of Mineralogy
4. Manual of Mineralogy by Cornelis Klein and Barbara Dutrow (23rd Edition)
5. Earth Materials: Introduction to Mineralogy and Petrology by Cornelis Klein and Anthony Philpotts (2nd Edition)
6. A-Level Geology — Mineralogy