As a result of fishing in competitions I have got used to measuring fish that I catch rather than weighing them. It’s quick and simple and of course puts little extra stress on the fish so that is all good. The process of course does have its short comings in that you don’t know how much the fish weighted and that is often interesting particularly for bigger fish. Well that’s no longer the case because I have adapted a mathematical process called a ‘power law equation’ to allow me to calculate the weight of fish from just one or two measurements.

It’s not 100% correct but you may be surprised to know that measuring fish by scales is often even less accurate. The problem with scales is that unless regularly calobrated they can be out significantly. Chances are that if you weigh a weight of 1 kilogram on several different scales you will get several different weights, I certainly did. In my test 90% of the results were within a range of 880 grams to 1.14 grams and on average negatively skewed for a 1 kilogram weight but for a 2 kilogram weight the margin of error was the opposite and positively skewed at 1.890 grams to 2.29 grams.

Believe it or not the calculation that follows is more consistent and the margin of error is often less.

A trout generally grows longer and heavier as time passes. If the rate of growth was linear then all you would have to do would be to multiply the length of a trout by a given factor as represented below.

That relationship over time between the length of a trout and its weight is unfortunately a non-linear relationship so it’s not just a matter of multiplying the length by a standard factor. What you need is an equation that take into account the non-linear variables as shown in the ‘power law equation” below which shows the relationship of trout length to average weight.

The basic ‘power law equation’ that I have been using to determine the average weight of a trout of a given length is as set out below.

Weight = cLp
When:
c=0.0000197
L=The length of the fish from the tip of the nose to the tip of tail with the fish laid flat
p=The power of 2.70 (for a standard trout) by which you need to multiply L by

The result is in kilograms so for pounds multiply that result by 2.2046.

So for example the average weight of trout 20cm, 30cm, 45cm and 60cm is calculated as follows:

20cm weight = .0000197 x (20x20x(20×0.7))
= .0000197 x (20x20x14)
= .0000197 x 5600
= 0.11 kilogram or 0.242 pounds

30cm weight = .0000197 x (30x30x(30 x0.7)
= .0000197 x (30x30x21)
= .0000197 x 18900
= 0.372 kilogram or 0.820 pounds

45cm weight = .0000197 x (45x45x(45×0.7)
= .0000197 x (45x45x31.5)
= .0000197 x 63787
= 1.26 kilogram or 2.768 pounds

60cm weight = .0000197 x (60x60x(60×0.7))
= .0000197 x (60x60x42)
= .000197 x 129680
= 2.97 kilogram or 6.67 pounds

If you want a more accurate estimate of a trout’s weight you will have to modify the exponent ‘p’ to filter out some of the ‘non-linear’ variables related to the condition of the fish as determined by its diameter at the largest girth.

Over time I have found that the average trout (that I have encountered and measured) have a length to diameter relationship which is very close to 3:1.8. This means that if it’s length is 60cm on average you should expect its diameter at its widest girth to be 36cm. The adjustment you make to the ‘p’ exponent to mitigate the effect of the ‘non-linear’ variables acknowledges that the sample trout being measured may not have the proportions of 3:1.8 which have been used as the average or standard.

I also noted that the movements in weight of trout above and below the average behaves differently. Trout in better than average condition put weight on slowly in response to available food and environmental criteria. The inverse does not apply to trout in poorer condition than the average. Unless the factor/s that caused the poorer than average condition are resolved trout tend to loose condition and weight very quickly. Accordingly the exponent ‘p’ for trout above the average increases at increments smaller than the increments of fall for trout that are below the average weight for size and are suffering due to age, sickness, injury or unfavourable environmental circumstances. That is reflected in the increment of increase in ‘p’ above trout of average condition being 0.05 whereas for trout below average condition the increment of decrease in ‘p’ is 0.10.

What this means is that if a trout does not meet the profile of length to diameter of 3:1.8 for an average trout and your looking for a more accurate estimate of weight change the ‘p’ exponent to the following:

Proportions:
Top quality fish 3:2.0 p=2.8
Better than average fish 3:1.9 p=2.75
Average condition 3:1.8 p=2.7
Thinner than average fish 3:1.7 p=2.5
Poor condition slabby fish 3:1.6 p=2.4

So for example the calculated weight of a “deep” and a “slabby” 60cm trout will be closer to the following:

Top quality fish with 3:2.0 proportions:

60cm weight = .0000197 x (60x60x(60×0.8))
= .0000197 x (60x60x48)
= .000197 x 172800
= 3.40 kilogram or 7.5 pounds

Standard trout with 3:1.8 proportions:

60cm weight = .0000197 x (60x60x(60×0.7))
= .0000197 x (60x60x42)
= .000197 x 151200
= 2.99 kilogram or 6.67 pounds

“Slabby” fish with 3:1.7 proportions:

60cm weight = .0000197 x (60x60x(60×0.4))
= .0000197 x (60x60x24)
= .000197 x 86400
= 1.70 kilogram or 3.75 pounds

Give it a go and compare the results to a set of calibrated scales … I am sure you will be pleasantly surprised.

Regards,
Chatto