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# Punnett Square Calculator

A Punnett Square shows the genotype^{*}s two individuals can produce when crossed. To draw a square, write all possible allele^{*} combinations one parent can contribute to its gametes across the top of a box and all possible allele combinations from the other parent down the left side. The allele combinations along the top and sides become labels for rows and columns within the square. Complete the genotypes in the square by filling it in with the alleles from each parent. Since all allele combinations are equally likely to occur, a Punnett Square predicts the probability of a cross producing each genotype.

Cross:

Parent 1:

Parent 2:

Show:

Genotype

Ratio

A single trait Punnett Square tracks two alleles for each parent. The square has two rows and two columns. Adding more traits increases the size of the Punnett Square. Assuming that all traits exhibit independent assortment, the number of allele combinations an individual can produce is two raised to the power of the number of traits. For two traits, an individual can produce 4 allele combinations (2^2). Three traits produce 8 combinations (2^3). Independent assortment typically means the genes are on different chromosomes. If the genes for the two traits are on the same chromosome, alleles for each trait will always appear in the same combinations (ignoring recombination).

With one row or column for each allele combination, the total number of boxes in a Punnett Square equals the number of rows times the number of columns. Multi-trait Punnett Squares are large. A three trait square has 64 boxes. A four trait square has 256 boxes.

The genotype in each box is equally likely to be produced from a cross. A two-trait Punnett Square has 16 boxes. The probability of a cross producing a genotype in any box is 1 in 16. If the same genotype is present in two boxes, its probability of occurring doubles to 1/8 (1/16 + 1/16).

If one of the parents is a homozygote for one or more traits, the Punnett Square still contains the same number of boxes, but the total number of unique allele combinations is 2 raised to the power of the number of traits for which the parent is heterozygous.

A commonly discussed Punnett Square is the dihybrid cross. A dihybrid cross tracks two traits. Both parents are heterozygous, and one allele for each trait exhibits complete dominance^{*}. This means that both parents have recessive alleles, but exhibit the dominant phenotype. The phenotype ratio predicted for dihybrid cross is 9:3:3:1. Of the sixteen possible allele combinations:

- Nine combinations produce offspring with both dominant phenotypes.
- Three combinations each produce offspring with one dominant and one recessive phenotype.
- One combination produces a double recessive offspring. This pattern only occurs when both traits have a dominant allele. With no dominant alleles, more phenotypes are possible, and the phenotype probabilities match the genotype probabilities.

A simpler pattern arises when one of the parents is homozygous for all traits. In this case, the alleles contributed by the heterozygous parent drives all of the variability. A two trait cross between a heterozygous and a homozygous individual generates four phenotypes, each of which are equally likely to occur.

More complicated patterns can be examined. In an extreme case when more than two alleles exists for each trait and the parents do not possess same alleles, the total number of genotypes equals the number of boxes in the Punnett Square.

It is possible to generate Punnett squares for more that two traits, but they are difficult to draw and interpret. A Punnett Square for a tetrahybrid cross contains 256 boxes with 16 phenotypes and 81 genotypes. A third allele for any one of the traits increases the number of genotypes from 81 to 108.

Given this complexity, Punnett Squares are not the best method for calculating genotype and phenotype ratios for crosses involving more than one trait.

Test your understanding with the Punnett Square Calculator Problem Set.

**Video Overview**

**Related Content**

## Comments

## Love how you can do many

Love how you can do many traits! Captures what it aims to do really good.

...and it runs on linux!!!

## It also runs on

windows, mac, android and iOS.

I even tried it on my daughter's DSi, but the DSi ran out of memory before the page loaded completely.

## Punnett Square Calculator

For those who are interested Here's you can download punnett square calculator:Punnett Square Calculator

## Robust

looks like a robust resource for Windows users. How much work would it be to port something like that to android or iOS?

## Bifido

Yes, it will be a little difficult ported it to Android and iOs. But Bifido is professional tool - not just simple calculator. Can this calculator do, what Bifido can? And by the way, Bifido is Qt application - so it can be easily ported to Mac or Linux.

## Question

In the last seconds of the video the narrator says:

“Given this complexity, Punnett Squares are not the best method for calculating genotype* and phenotype* ratios for crosses involving more than one trait.”

Okay, what is the best method?

## Answer

Because of the sheer number of allele* combinations possible when tracking multiple, independently assorting traits, we usually don't calculate the probability for all genotype*s. It is more common to focus on a small set of possible genotypes. For example, you might be asked to calculate the probability that a specific paring will result in offspring containing one or more recessive traits. In this case, we can ignore all but a few genotypes and avoid generating a huge Punnett Square.

Instead, we calculate the probability for each trait individually using single trait Punnett Squares. Then, given independent assortment, we can multiply the individual probabilities together to find the probability of producing specific multi-trait combinations.

Consider a tryhibrid cross AaBbCb x AaBbCc. If we want to know the probability of producing a triple heterozygous offspring (AaBbCc). We first treat each trait separately and determine that there is a 50% (0.5) chance that an offspring will be heterozygous for each of the traits A, B and C.

The probability that an offspring will be heterozygous for all three traits is the product of the individual probabilities: 0.5 x 0.5 x 0.5 = 0.125. There is a 12.5% chance that the mating will produce a triple heterozygous offspring.

Once we know all of the single trait probabilities, it is easy to calculate additional multi-trait probabilities. The probability of the cross above (AaBbCc x AaBbCc) producing AAbbCc is:

(0.25 for AA) times (0.25 for bb) times (0.5 for Cc) = 0.25 x 0.25 x 0.5 = 0.03125 or 3.125%

The key thing to grasp is that independent assortment allows us to multiply individual trait probabilities to find multi-trait probabilities.

If for some reason you want to calculate the probability for every genotype in a multi-trait cross, it is still better to calculate them by multiplying the single trait probabilities. Because, it is easy to make mistakes when drawing large Punnett Squares.

There is a third technique involving drawing branching diagrams, but I don't use it.

## Thank you. That was very

Thank you. That was very helpful.

## Error in 5x5 square computation?

Either I am reading this wrong, or there is an error in the program when you take it up to 5x5.

Reading across the top row there when you do a cross of AaBbCcDdEe × AaBbCcDdEe I am only seeing 30 uinque entries across the top. It appears that ABcDe and aBcDe are missing and replaced by duplications of other combinations.

## Fixed

You were right, there was a typo in an aray. What did I say about it being easy to make mistakes drawing such large squares?

## Quite true

Your point is driven home.

## AP Biology

I'm trying to do my homework and I don't have the time to do the punnett squares.

## Phenotype ratio error

The Punnett Square display for Phenotype* Ratio/% is incorrect if we are showing Mendelian (Dominant/Recessive) genetics*. For example: Aa x Aa cross would produce a Genotype* of 25% AA : 50% Aa : 25% aa, but the Phenotype would be 75% "A"(AA+Aa) : 25% "a" (aa).

## Can't reproduce

@Gmager: Thanks for the feedback. I am unable to reproduce your error. If I set the number of traits to 1, have two heterozygous (Aa) parents, make either allele* (A or a) the dominant allele and show Phenotype* percent or ratio, I get two distinct phenotypes with the appropriate frequencies.

If the radio button for dominant allele is left at the default setting of "None", the calculator assumes that Aa produces an intermediate phenotype. Under these conditions the phenotype probability matches the genotype* probability (25:50:25)

## SCIENCE

HOW DO I DO THE PUNNETT SQUEAR..THANK YOU AND HAVE A GREAT DAY SINCERLY BARONNA FREEMAN

## The way it works is like a

The way it works is like a multiplication table. I hope i answered your question.

## This saved my life!!!! thank

This saved my life!!!! thank you!

## Calculating Phenotypic Raitios for multiple traites

Is there another way to determine Phenotypic ratios without using a punnett square. I know how to calculate the number of traite categories but not the ratios in each.

## Calculating individual phenotypic ratios

You can calculate phenotypic ratios using the process described for genotypic ratios in this comment. Does this answer your question?

## Share code?

Would you consider sharing the code, or at least the algorithm, you use in calculating the results of the crosses? I'm trying to come up with something similar in R; but, rather than produce a Punnett Square, it will feed the numerical results of extremely large numbers of loci into calculations following up on Fisher's (1918) polygenic model. I'm trying to avoid a brute force solution, but I'm embarassed I haven't found a simple algorithm yet!

Thanks in advance, and really nice work on this page!

## contact me

DGM - I will give you whatever help I can. Send me a message using the site contact form: http://www.scienceprimer.com/contact

## Hmm

Your video go's way to fast. I don't know what kind of audience it's directed at, but I've done punnett squares before and I can't follow anything you said. It's explaining how to do a math equation in four minutes.

## Overview

John, thanks for the input. There is quite a bit of information packed into the video. As the title states, it is an overview. If you want to gain a good understanding of the concepts covered, read over the material on this page, spend some time with the calculator and take a look at the links under "related content".

## Wonderful Program!

This is an excellent thing I didn't (unfortunately) know existed in my high school biology course! I use it all the time now for my college biology homework! :)

## punnett

great

## Told the phenotype ratios are wrong by professor

Hi, I was told you cannot write phenotype*s in "GG" Gg" format. Why are you expressing them this way? I was told my ratios were completely wrong since my tutor told me to check my work here. Now, I am told there is no way a phenotype is EVER expressed like that for a ratio. It was by a professor with their doctorate. Could you advise what you mean by your answers? I got 25% of my grade wrong because I used the phentype ratio you suggest. Thank you. I don't mind to mean unappreciative.

## Phenotypes labels must be translated for each specific case

## Thank you

I see exactly what you are saying. Thank you for your kind comment. The problem lies in my not knowing how to express the phenotype* and not in your program. Thank you again.

## Is it possible to generate a

Is it possible to generate a downloadable image file of the punnett square?

## The square is text not an image

The easiest thing to do is to scale the square to the size you want and take a screen shot.

There is no easy alternative because the square is not rendered as an image. It is a set of text boxes arranged in rows and columns. If you know anything about html, each box is a div elelment with a colored background.

If you are comfortable going into the source, you can grab the content of the div with the id "squarePositionDiv" and paste it into another html file.

## So good!

Thanks for this! i'm from south america and with this make my biology homework more easier... Sorry for my bad english! :) Graciasss!

## science

need a picture of squaresi

## Good Job!

Verry Helpful

## calculator

would love codominance and/or incomplete

## Set dominant trait to none

Codominance and/or incomplete dominance* patterns can be shown with the calculator by setting the dominant allele* to 'none' for the incomplete and co-dominant traits.

## Confused

Isnt there supposed to be a diffrence between genotype*s and phenotype*s with linked genes? just sayin

## Calculator assumes independent assortment

@rick: I am not sure what you are asking. The patterns shown assume independent assortment. The calculator doesn't work for linked genes.

## Punnett square for ADD.

Punnett square for ADD.

## What is this

I dont understand what it does though!

## I cant read the 5-trait cross

I cant read the 5-trait cross

## What are you trying to get?

You can see all of the genotype* or phenotype* frequencies by clicking the "show frequencies" button at the top

## Knowing how much Linux is

Knowing how much Linux is used in the science industry, it make me happy when websites provide interactive content that isn't platform dependant.

## Thanks

I try to be as platform neutral as possible. Of course, most of the site will not work with IE8... :-)

## Blood Type

is there a blood type punnet square calculator anywhere?

## Can use this calculator to get the genotypes

This calculator will give you the genotype*s for blood type crosses, but it can not deal with the codominance of the A and B allele*s. So, you'll have to calculate some of the phenotype* probablities on your own.

For example:

you get 4 genotypes:

AA, OA AB and OB. With AB codominance the pheotypes will be A, AB and B

Frequencies will be

A = AA + AO = 25% + 25% = 50%

B = OB = 25%

AB = AB = 25%

To make this work you need to remember that the genotypes AA and AO give the same phenotype as do BB and BO.

## Punnet square help!!

I have been trying to make a punnet squarre as slisted below. Did it myself and was told it was wrong! Used this calculater ans was told it was wrong. Can anyone help!

Use a punnett square to figure out the results and type in the phenotype* ratios including the types (tall green or what ever is correct) for the following crosses, a cross between the following parents TTyy x TtYy

## Convert allele patterns to phenotype labels

Marie,

I am sorry you are having trouble. Are you converting the allele* labels from the phenotype* frequencies to the actual phenotypes descriptions? See this comment from above for more context: http://scienceprimer.com/comment/937#comment-937

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