The Cardio Formula

A popular formula for determining the heart rate ranges for the individual stress zones is the Karvonen formula. This formula is named after the Finn Martti Karvonen (1918 – 2008). Karvonen received his doctorate in 1945 at the University of Helsinki to Dr. med., 1950 followed the doctorate in Physiology at the University of Cambridge. He then became a lecturer in sports medicine in Helsinki. He was also an advisor to the World Health Organization (WHO). He led countless clinical and epidemiological studies.

Karvonen has received numerous awards for his achievements, especially in sports medicine, especially from sports medicine associations in Finland, Germany, and the USA. Karvonen is best known for his formula of the same name, which takes the resting pulse and the maximum pulse into account.

The carving formula is:

TrainingsHF = (220 - age - resting pulse) * Factor + resting pulse


Calculation example cardio formula

Here the calculation example of a 40 year old man with resting pulse 60 to determine the heart rate for his GA1 range (factor 0.6 to 0.7):

Calculation of the lower value (factor 0.6)

TrainingsHF = (220 - 40 - 60) * 0,6 + 60
The values in brackets are calculated first:
TrainingHF = 120 * 0.6 + 60
First the product has to be calculated ("dot before line calculation"):
TrainingHF = 72 + 60
Finally add both values:
TrainingHF = 132

Calculation of the upper value (factor 0.7)

TrainingsHF = (220 - 40 - 60) * 0,7 + 60
The values in brackets are calculated first:
TrainingHF = 120 * 0,7 + 60
First, the product must be calculated ("dot before line calculation"):
TrainingHF = 84 + 60
Add both values at the end:
TrainingHF = 144

Result: The heart rate range for the GA1 stress zone is between 132-144.

ECG Diagram


Determination of the resting pulse

The determination of the resting pulse is very easy. You have the following options for measuring the pulse:

  • Per finger on the thumb side of the wrist or side of the neck,
  • or simply put on the heart rate monitor (absolutely with chest strap).

Measurements are taken lying down; best in the morning before getting up or after at least 10 minutes of rest. You should take care to be relaxed and not to move. Even small movements / internal tension can significantly increase the resting pulse.


Determination of the maximum heart rate (HFmax)

There are also several methods for determining the HFmax:

Feel the pulse on the artery
The pulse can be easily felt on the artery
  • rule of thumb 220 minus age.
  • Maximum cardiovascular load until exhaustion, then measure pulse immediately. It is imperative that the measurement is made during maximum load. Examples for a maximum load are e.g. several sprints, speed runs, ergometers with high increasing wattage.
The determination of HFmax with the second method involves a high risk of serious damage to health. I personally advise untrained people against this method!!


Alternatives to the carving formula

The Karvonen formula contains some inaccuracies in the determination of resting pulse and HFmax. It does not take into account the individual condition and constitution of the individual person. Therefore, its accuracy and its benefit for endurance sports are also controversial.

The current standard for heart rate measurement is the lactate diagnostics and the spiroergometry.


heart rates – load zones

In endurance sports, the following stress zones have become generally accepted.

The designations of the individual load zones vary according to the literature. The percentages also vary by up to 5% depending on the literature. A detailed description of the individual stress zones can be found in the article stress zones.

load zone% of maximum heart ratefactor
Compensation (Recom)Up to 60 %Up to 0.6
Basic endurance 1 (GA1)60 % to 70 %0.6 to 0.7
Basic endurance 2 (GA2)70 % to 80 %0.7 to 0.8
Development range (EB)80 % to 90 %0.8 to 0.9
Peak range (SB)above 90 %About 0.9

Here you find the suitable training units for Run beginners, Recreational runners, Run beginners href=”″>, Recreational runners, Hobby runners, and ambitious hobby runners.

This post is also available in: German

William C. Hilberg
As an author, Mr. Hilberg has published several papers on health issues that have gained international recognition. He is close to nature and loves the seclusion and activity as a freelance journalist. In his function as editor William C. Hilberg manages the entire content of PENP. Our team greatly appreciates his expertise and is proud to have him on board.