Lambda Calculator - Brettschneider Equation  (or how to determine AFR accurately)

The Brettschneider equation is the de-facto standard method used to calculate the normalized air/fuel balance (Lambda) for domestic and international I&M inspection programs. It is taken from a paper written by Dr. Johannes Brettschneider, at Robert Bosch in 1979 and published in "Bosch technische Berichte", Vol 6 (1979) N0. 4, Pgs 177-186. In the paper, Dr. Brettschneider established a method to calculate Lambda (Balance of Oxygen to Fuel) by comparing the ratio of oxygen molecules to carbon and hydrogen molecules in the exhaust.
USA Europe

Note: The USA and Europe choices are to account for the use of different values of Hcv and Ocv (see values below)










CO %
  • FIRST ADVANTAGE: The exhaust gas sample can be taken before or after the catalytic converter.    .
  • SECOND ADVANTAGE: The AFR displayed compensates for the degree of combustion - due to combustion inefficiencies, ignition timing, misfire, or poor CAT action.
  • The exhaust system must be free of any air leaks.
  • If equipped with Exhaust Air Injection (AI) it should be disabled.
HC ppm
CO2 %
O2 %

Lambda Calculation Lambda A/F Ratio
using 4-Gas Measurement
using 5-Gas Measurement
NOx ppm

For Gasoline, K1 is 6.0, Hcv is about 1.800 (depending on the actual mix), and Ocv is 0.017 for oxygenated fuels. The equation above compares the sources of oxygen in the numerator, and all of the sources of carbon and hydrogen in the denominator. (The ratio of unburned hydrogen to water is determined by the ratio of CO to CO2 in the numerator).

The Lambda result is a dimensionless value that indicates the balance of air to fuel compared to the stoichometric point, where Lambda = 1.000. As an example, Lambda of 1.010 means there is 1% too much oxygen (1% "lean" of stoichometric, not 1% lean of where the engine wants to be) and 0.990 means there is 1% too little oxygen (1% rich of stoicometric, not 1% richer than where the engine wants to be) in the exhaust gas makeup.

For gasoline, Lambda x 14.71 is the air/fuel mass ratio as for gasoline, at the perfect stoichometric point the A/F mass ratio is 14.71 (1.00 Lambda).

That does not mean that and engine actually wants anything like 14.7:1, it just means that that's what the exhaust gases contain to back out the AFR,  given the amount of air and fuel delivered and burned to some efficiency rate. When tuning an existing engine, 14.7:1 is essentially, a value that is only useful in a chemistry class.

This Lambda calculation determines the relative balance of Oxygen to Combustibles in the exhaust gas by direct measurement of oxygen and combustibles bearing gases. Lambda calculated in this way is independent of the degree of combustion - whether due to combustion inefficiencies, ignition timing, misfire, or poor CAT action, and is a good witness of the effectiveness of the vehicle EMS fuel control (lambda) closed loop system.

Also, because of the independence to combustion efficiency, it does not matter whether pre or post CAT exhaust gases are used for the calculation.

Exhaust Air Leaks
However, excess air caused by exhaust system air leaks, or air injection will cause the exhaust-gas-calculated Lambda to indicate leaner than actual values. These air dilution conditions are usually indicated by high O2 readings in the exhaust stream along with an overall reduction in the concentration of the other gases. To improve the correlation of the EGA Lambda to the Engine Management System mixture control point, air injection should be disabled, and exhaust air leaks should be corrected.

Reprinted by Factory Pro Courtesy of Robert Schrader - Bridge Analyzers, Inc. Copyright Bridge Analyzers, Inc.