Retrograde Extrapolation: Calculating What Your BAC Was in the Past
Retrograde extrapolation = BAC_measured + (0.015 × hours). Use the Alcomato calculator to model your BAC over time — the same math in forward direction.
Model Your BAC Over Time →Retrograde extrapolation is the forensic technique of calculating what a person's BAC was at an earlier point in time, based on a BAC reading taken later. It is used by prosecutors and defence attorneys in DUI cases to argue what BAC was at the time of driving, not just at the time of the breathalyzer test. Understanding the math can be critical for understanding DUI cases and the limits of BAC evidence.
What Is Retrograde Extrapolation?
When someone is stopped for suspected DUI, the breathalyzer test happens after the stop — sometimes 30 minutes to 2 hours after the alleged driving. The question becomes: what was the BAC when they were actually driving? Retrograde extrapolation works backwards from the measured BAC, adding back the alcohol that was metabolised in the intervening time.
- Used by prosecution: To argue that BAC at time of driving was higher than the test shows (because metabolism reduced it between driving and testing).
- Used by defence: To argue that BAC was rising at the time of driving (still absorbing alcohol), so the test reading was actually higher than when driving.
The Formula: BAC_past = BAC_measured + (Rate × Hours)
BAC at past time = BAC measured + (elimination rate × hours elapsed)
Where:
- BAC measured: The actual breathalyzer or blood test result.
- Elimination rate: Typically 0.015% per hour (commonly used forensic standard). Range: 0.010%–0.020%/hr.
- Hours elapsed: Time between the incident and the BAC test.
Use the Alcomato calculator to model your BAC over time — including how it drops after you stop drinking, which is the same math as retrograde extrapolation in reverse.
Model Your BAC Over Time →Why 0.015% Per Hour Is Used
The 0.015%/hr rate is the population average for alcohol elimination, derived from hundreds of studies. However, individual elimination rates vary from approximately 0.010% to 0.020% per hour based on:
- Liver enzyme activity (ADH and ALDH levels)
- Chronic alcohol consumption history (heavy drinkers eliminate faster)
- Body composition and gender
- Fed/fasted state and food composition
In DUI cases, the range of possible rates (0.010–0.020) means retrograde calculations have a wide uncertainty band. A 2-hour retrograde at 0.010/hr adds only 0.020% to the measured value, while at 0.020/hr it adds 0.040% — a difference that can determine guilt or innocence.
Worked Example: What Was My BAC at 10pm?
Scenario: Breathalyzer reads 0.05% at midnight. Person stopped drinking at 10pm (2 hours before test).
| Rate Used | Retrograde Estimate at 10pm | Was Driving Over Limit? |
|---|---|---|
| 0.010%/hr (low) | 0.05 + (0.010 × 2) = 0.070% | Below 0.08% — under limit |
| 0.015%/hr (average) | 0.05 + (0.015 × 2) = 0.080% | Exactly at 0.08% limit |
| 0.020%/hr (high) | 0.05 + (0.020 × 2) = 0.090% | Over 0.08% limit |
The same measured BAC of 0.05% leads to three different legal conclusions depending on which elimination rate is used — this is why retrograde extrapolation is contested in courts.
Limitations of Retrograde Extrapolation
The Rising BAC Problem
If the person was still absorbing alcohol when driving (last drink was within 60–90 minutes of driving), their BAC was lower at the time of driving than at the time of testing. In this case, retrograde extrapolation by prosecution would overestimate the driving BAC. This is a recognised defence argument.
Individual Variability
The individual's actual elimination rate is unknown without sequential BAC measurements. Using the population average (0.015%/hr) introduces error. Courts must decide whether this uncertainty creates reasonable doubt. See our Widmark formula article for more on individual variability factors.
Want to see how your BAC changes over time after your last drink? The calculator models both rising and falling BAC phases.
Model BAC Over Time →How Courts Use This Calculation
Most US states allow retrograde extrapolation evidence in DUI cases, though admissibility rules vary. The prosecution must typically establish the foundation facts: time of driving, time of last drink, time of test, and that the defendant was in the elimination phase (not still absorbing). Some states require the expert to account for the uncertainty range. Defendants can challenge the calculation through expert testimony on individual elimination rate variability and the rising BAC defence.
Frequently Asked Questions
Can retrograde extrapolation add time in the future (antegrade)?
Yes — antegrade extrapolation estimates future BAC from a known reading, adding time forward instead of backward. If you blew 0.08% and want to know when you will reach 0.00%, the same math applies: 0.08 / 0.015 ≈ 5.3 hours. The Alcomato calculator performs this calculation automatically in the "hours until sober" output.
What does "retrograde extrapolation" assume about metabolism?
It assumes zero-order kinetics — constant elimination rate regardless of BAC level. This is accurate above approximately 0.02% BAC. Below that level, Michaelis-Menten kinetics apply and elimination slows non-linearly. For BAC values above 0.05%, zero-order kinetics is a valid assumption for forensic purposes.
Is retrograde extrapolation the same as the Widmark formula?
They are related but different. The Widmark formula estimates BAC from drinks consumed. Retrograde extrapolation starts from a measured BAC and works backwards in time. Both use the same 0.015%/hr elimination rate. See our detailed explainer on the Widmark formula for the complete forward-direction calculation.
The same math that forensic experts use to calculate past BAC is in the Alcomato calculator — just in forward direction.
Calculate Your BAC Now →Disclaimer: This article provides educational information only. It does not constitute medical or legal advice. BAC calculators provide estimates, not exact measurements. Individual BAC varies based on numerous factors including body composition, metabolism, food intake, medications, and health conditions. Never rely solely on calculators to determine if you are safe to drive. The only safe BAC for driving is 0.00%. Always use alternative transportation after consuming alcohol. If you struggle with alcohol use, consult a healthcare professional or contact SAMHSA's National Helpline at 1-800-662-4357.