🧪 Forensic Blood Alcohol Retrograde Extrapolation Simulator

Incident-Time BAC — The Hidden Number

The true BAC at the moment of driving is never directly measured.

• 0.08%: Legal limit (most US states) (per se DUI threshold)
• 30–90 min: Peak BAC delay (absorption lag after last drink)
• 0.010–0.020%/hr: Typical β range (adult elimination rate)
• 1932: Method introduced (Widmark back-calculation)

The incident BAC

True BAC at the incident is unknown and unmeasured.

Why it matters

Charges hinge on BAC while driving, not later.

The forensic goal

Extrapolation estimates this hidden earlier value.

Time Elapses Between Incident and Sample

The delay before blood is drawn is itself a critical variable.

• 1–3 hr: Typical draw delay (stop to blood draw)
• Zero-order: Kinetics after absorption (roughly linear decline)
• ~0.015%: Average hourly drop (population mean rate)
• ~4–6 hr: Reliable extrapolation window (beyond this, error grows fast)

The elapsed gap

Hours pass between the incident and the blood draw.

Continued elimination

The body keeps metabolizing alcohol during this gap.

Why delay matters

A longer gap means a larger backward correction.

Sample BAC Is Measured in the Lab

A single verified number anchors the entire backward calculation.

• 5+: Chain-of-custody steps (draw, seal, label, transport, log)
• Sodium fluoride: Tube preservative (prevents fermentation artifacts)
• Headspace GC: Standard lab method (gas chromatography, FID detector)
• ±0.005%: Reporting uncertainty (typical forensic lab margin)

Sample collection

A blood sample is drawn at the later, known time.

Laboratory analysis

Gas chromatography measures ethanol concentration precisely.

The known anchor

This measured value anchors the extrapolation calculation.

A Steady Elimination Rate Is Applied

Widmark's equation adds back what the body already cleared.

• 0.010–0.020%/hr: Rate range used (individual variation)
• C0 = Ct + βt: Core formula (Widmark retrograde equation)
• 0.015%/hr: Average male β (commonly cited default)
• Post-absorptive: Key assumption (absorption phase already complete)

The elimination rate

Alcohol clears the blood at a roughly constant hourly rate.

Widmark's equation

Incident BAC equals sample BAC plus rate times hours.

Rate uncertainty

The true individual rate is rarely known for certain.

Retrograde Estimate — Extrapolating Backward

The elimination line is projected back to reveal the incident BAC.

• Backward: Projection direction (sample time toward incident time)
• Expert testimony: Court requirement (toxicologist explains assumptions)
• Range, not point: Best practice (low/high β bounds reported)
• Mata v. State: Landmark case (set extrapolation evidentiary standards)

Backward projection

The line is projected backward from the sample point.

The estimated value

This reveals the probable BAC at incident time.

Legal application

Courts use this estimate to test the legal-limit claim.