Gemstone Price Calculator
Estimate fair market value for natural gemstones using the Alwadhi Power-Law
Based on the research of Khalilah A. Al-Wadhi · Read the paper · GitHub
Diamond Details
Ruby Details
Sapphire Details
Emerald Details
Alexandrite Details
What does the exponent mean?
Each gemstone type has its own "scaling exponent" — think of it as how steeply price climbs as the stone gets bigger. A higher number means large stones are dramatically more valuable than small ones. A lower number means size matters less.
For example, alexandrite (2.12) is one of the rarest gemstones on earth. A 2-carat alexandrite isn't just twice the price of a 1-carat — it's about 4.3 times more. For aquamarine (1.46), the jump is gentler: a 2-carat is about 2.75 times a 1-carat.
Diamond Shape Premiums
Round brilliants command the highest prices due to superior light performance and maximum rough-to-polished yield demand. Fancy shapes trade at a discount — hearts and pears show the largest discount because of lower demand and cutting waste.
Offline Pricing Tool
For miners, dealers, and anyone who needs to price stones without an internet connection. This is a standalone bash script
that runs on any Mac, Linux, or Windows (WSL) machine. Only requires bc (pre-installed on almost everything).
Download alwadhi_pricer.sh from GitHub, then:
# Make it executable
chmod +x alwadhi_pricer.sh
# Price a single stone
./alwadhi_pricer.sh price diamond 1.50 shape=round
./alwadhi_pricer.sh price ruby 2.00 origin=burma treatment=untreated colour=pigeon_blood
./alwadhi_pricer.sh price sapphire 3.00 colour=kashmir
./alwadhi_pricer.sh price alexandrite 0.80
# Price a whole parcel from CSV
./alwadhi_pricer.sh batch my_inventory.csv priced_output.csv
# See all parameters
./alwadhi_pricer.sh params
CSV Batch Format
Create a .csv file with one stone per line. Columns: gemstone type, weight, then any modifiers as key=value pairs:
diamond,1.00,shape=round
diamond,2.50,shape=princess
ruby,1.50,origin=burma,treatment=heated,colour=vivid_red
sapphire,2.00,colour=kashmir
emerald,1.00
alexandrite,1.00
paraiba,0.50
tanzanite,3.00
Quick One-Liner (no script needed)
If you just need a fast number and don't want to download anything:
# Diamond: P = 3127.43 * W^1.725 * Cs
echo "scale=2; 3127.43 * e(1.725 * l(1.50)) * 1.000" | bc -l
# Ruby (Burmese, pigeon blood, unheated):
# P = 4200 * W^1.89 * origin * treatment * colour
echo "scale=2; 4200 * e(1.89 * l(2.00)) * 2.5 * 3.0 * 2.0" | bc -l
# Sapphire (Kashmir, cornflower, unheated):
echo "scale=2; 2450 * e(1.62 * l(3.00)) * 3.5 * 2.2 * 2.5" | bc -l
# Generic formula: P = B * e(alpha * ln(W)) * modifiers
# Use: echo "scale=2; B * e(ALPHA * l(WEIGHT)) * M1 * M2" | bc -l
The Short Version
Bigger gemstones aren't just proportionally more expensive — they're exponentially more expensive. A 2-carat diamond doesn't cost twice what a 1-carat costs. It costs about 3.3 times as much.
The Alwadhi Power-Law captures this relationship with a simple formula that works across all major natural gemstone types. It was validated on over 1.2 million real transactions from global markets including New York, Antwerp, Mumbai, Hong Kong, and Dubai.
The Formula
Price = Base × Weightexponent × Quality Factors
Each gemstone type has its own base price and exponent, calibrated from market data. Quality factors adjust for shape, colour, clarity, origin, treatment, and other attributes specific to that stone type.
Why Does This Work?
Large natural gemstones are geologically rare — the earth simply produces far fewer big crystals than small ones. This scarcity follows a mathematical pattern (a power law), and prices reflect that same pattern. The rarer the gemstone type (alexandrite, Paraiba tourmaline), the steeper the price curve.
Important Caveats
This model applies to natural gemstones only. Lab-grown diamonds follow manufacturing cost curves, not geological scarcity. Prices reflect wholesale/trade benchmarks — retail may be significantly higher. Individual stones are unique; provenance, specific inclusions, and market timing all matter.
Full paper: DOI 10.5281/zenodo.17437226
Code and data: GitHub repository
Licence: CC BY 4.0 International
Why the Alwadhi Power-Law?
The Rapaport Diamond Price List has been the industry benchmark since 1978. It serves an important role as a shared language for diamond dealers worldwide. But as a pricing tool, it has structural limitations that the Alwadhi Power-Law framework addresses directly.
1. All Gemstones — Not Just Diamonds
Rapaport covers diamonds only (round and pear shapes, with pear as a proxy for fancies). There is no Rapaport list for rubies, sapphires, emeralds, or any coloured stone.
The Alwadhi Power-Law covers 10 gemstone categories — diamond, ruby, sapphire, emerald, alexandrite, Paraíba tourmaline, padparadscha, spinel, tanzanite, and aquamarine — each with its own empirically calibrated exponent. If you deal in coloured stones, this framework fills a gap that simply doesn't have an equivalent.
2. Fully Transparent Methodology
Nobody outside Rapaport's organisation knows exactly how Martin Rapaport arrives at his numbers. The methodology is proprietary and unpublished — and Rapaport himself has financial interests in the diamond trade, creating a clear conflict of interest.
The Alwadhi Power-Law is fully open: every parameter is published, the derivation from scarcity economics and fractal geology is shown from first principles, data processing is disclosed, and independent replication is encouraged. The entire framework is released under CC BY 4.0 — freely auditable by anyone.
3. Real Transaction Data — Not Asking Prices
Rapaport prices are not actual transaction prices. They reflect seller asking prices for fine-cut stones in cash deals. Dealers then negotiate discounts off the list — typically 20–40% below "Rap." As industry analysts have noted, Rapaport prices are "almost always higher than actual dealer transaction prices."
The Alwadhi model is calibrated on 1.2 million real transaction records across global markets (2019–2024), plus auction data from Christie's and Sotheby's. It reflects what stones actually sold for.
4. Continuous Pricing with Confidence Intervals
Rapaport is a discrete table — fixed size brackets, fixed colour/clarity cells. If your stone falls between brackets, you interpolate by feel. And you get a single number with no error band.
The power-law is a continuous mathematical function: enter any carat weight to the hundredth and receive a precise price with a 95% confidence interval (σres = 0.0856). A stone priced at $15,000 would show a likely range of ~$12,500–$17,700. That's critical for insurance valuations, portfolio risk, and dispute resolution.
5. A Scientific Law — Not Editorial Judgement
Rapaport is updated weekly based on one person's editorial assessment of market conditions.
The Alwadhi exponent α emerges from two independent theoretical pathways — scarcity economics and fractal scaling of geological formations. It achieves R² = 0.9874 (p < 10−15) in-sample and R² ≈ 0.986 out-of-sample, with stability confirmed across five global markets (New York, Antwerp, Mumbai, Hong Kong, Dubai) and across time (2019–2024). The 2025 revalidation on public data confirmed R² = 0.991.
6. Free, Offline, and Instant
A Rapaport subscription costs approximately US$125/month and requires internet access to retrieve each week's list.
The Alwadhi Power-Law is open-access, computes in 0.4ms (vs 28–128ms for machine learning alternatives), and can run in a simple bash script offline — useful for dealers in the field, miners, and auction houses without connectivity.
Where Rapaport Still Leads
Rapaport is the entrenched industry standard. Dealers worldwide quote prices as "Rap minus X%," so it functions as a shared language of trade. The Alwadhi Power-Law doesn't need to replace that language — it sits alongside it as the mathematical verification layer, providing the scientific rigour and gemstone breadth that a lookup table cannot.
Side-by-Side Summary
| Feature | Rapaport | Alwadhi Power-Law |
|---|---|---|
| Coverage | Diamonds only | 10 gemstone categories |
| Methodology | Proprietary / undisclosed | Open, peer-reviewed, CC BY 4.0 |
| Data source | Seller asking prices | 1.2M real transactions |
| Pricing type | Discrete grid / lookup table | Continuous formula |
| Confidence intervals | None | 95% CI included |
| Statistical fit | Not published | R² = 0.9874 |
| Conflict of interest | Publisher trades diamonds | Academic research — no trading |
| Cost | ~US$125/month | Free & open-access |
| Offline use | No (internet required) | Yes — runs in bash / 0.4ms |