This free HorRat calculator tells you in seconds whether your method precision is realistic for the level you measure. Check whether your analytical method’s precision is reasonable for the concentration you are measuring. Enter the level and your observed RSD (or paste replicate results) to get the Horwitz predicted RSD and the HorRat value, with an AOAC-based verdict.
How to use the HorRat Calculator
- Enter the mean concentration and pick its unit.
- Enter your observed precision as RSD % or SD, or paste replicate results and let the tool work it out.
- Choose the precision condition (reproducibility or repeatability) and the prediction model.
- Press Calculate HorRat to see the predicted RSD, the HorRat value and the verdict.
The HorRat calculator works in mass fraction, so mg/L and µg/L results in water can be entered as mg/kg and µg/kg. The acceptance ranges follow method performance guidance from AOAC INTERNATIONAL.
What is the HorRat value?
The Horwitz ratio (HorRat) compares the precision you actually get from a method with the precision predicted by the Horwitz equation for that concentration. William Horwitz found, from thousands of collaborative studies, that the between-lab relative standard deviation depends mostly on how much analyte is present, not on the method or matrix. The lower the concentration, the larger the RSD you should expect.
Formula used
How to read the result
| Condition | Acceptable HorRat | Typical meaning |
|---|---|---|
| Reproducibility (inter-laboratory) | 0.5 – 2.0 | Method precision is normal for this concentration |
| Repeatability (single laboratory) | 0.3 – 1.3 | Within-lab precision is in line with expectations |
| Above the range | > 2.0 (R) / > 1.3 (r) | Method or lab has a precision problem worth investigating |
| Below the range | < 0.5 (R) / < 0.3 (r) | Suspiciously good: too few results, excessive averaging or rounding |
These ranges follow AOAC INTERNATIONAL guidance for method validation. The Horwitz model does not work well for some cases, such as physical properties, empirical methods, very pure materials, and some trace analyses by highly selective techniques. Treat the HorRat as a sense check, not the only acceptance criterion.
Where labs use it
- Single-laboratory method validation for ISO/IEC 17025 accreditation
- Setting realistic target standard deviations for proficiency testing (σpt)
- Checking whether precision claims in a published method are credible
- Setting acceptance limits for duplicate analyses in routine QC
Frequently asked questions
What is an acceptable HorRat value?
For reproducibility data, a HorRat between 0.5 and 2.0 is generally acceptable. For repeatability (single-lab) data, AOAC uses 0.3 to 1.3.
Why does the Horwitz equation need the Thompson correction?
The original equation predicts unrealistically large RSDs below about 120 µg/kg (ppb). Thompson showed that real inter-lab RSDs level off near 22% at trace levels, and that the equation over-predicts at very high concentrations. The corrected model is widely used, for example in food proficiency testing.
What concentration unit should I use?
Any unit works. The calculator converts your value to a dimensionless mass fraction (for example 1 mg/kg = 0.000001), which is what the Horwitz equation needs.
Can I use the HorRat for water analysis in mg/L?
Yes. For dilute aqueous solutions, 1 mg/L is close enough to 1 mg/kg for this purpose.
What is the Horwitz equation?
The Horwitz equation predicts the between-laboratory relative standard deviation from concentration alone: PRSDR (%) = 2 × C−0.1505, where C is the mass fraction (1 mg/kg = 10⁻⁶). At 1 mg/kg it predicts about 16% RSD, and at 1% (10⁻²) about 4%.
How do I calculate the HorRat value by hand?
Divide your observed RSD by the predicted RSD: HorRat = RSDobs ÷ PRSD. An observed reproducibility RSD of 12% at 1 mg/kg (PRSD 16%) gives a HorRat of 0.75, inside the usual 0.5–2.0 range.
Related tools
For guidance only. Your method validation plan and accreditation body requirements take precedence. Built by an ISO/IEC 17025 laboratory professional.