This rather grandiosely named "Franking Combinations Calculator" is an online tool for working out all the possible combinations of values for a given postage rate that can be made up using a single set of stamps.

For example,the list at right shows the 21 possibilities for making up a 4d rate from a typical set of stamps that include the values ½d, 1d, 1½d, 2d, 2½d, 3d and 4d. This would correspond, for example, to all the ways to pay the 1950-57 4d basic rate for foreign surface/European all-up mail using the low values on issue at the time.

Using the Calculator

The general idea is to enter a list of possible values in the "Calculate using these values" box, enter the rate that you want to calculate combinations for, and click the "Calculate" button. The possible combinations will appear in the box underneath.

The format to use for entering the rate and the list values is basically as shown above, although it's fairly flexible. You can enter halfpences either as ".5" or as the more readable ½ character, whichever is easier to type (see below). The s/d/p suffixes can be omitted (£sd currency is assumed if you don't specify), and you can just use spaces to separate the values if you like, leaving out the commas (although in that case you will need to give values over 1s in whole pence – e.g. "15" not "1s 3d").

However, the quickest way is to use the "Quick select" options on the right. The "Set" dropdown lets you pick a named set of values, while the "Year" box lets you enter (or select using the arrows) a value from 1840 to 1980, and will fill in all the values on issue in that year.

Comments and suggestions welcome.

Number of Combinations

The numbers are subject to the "combinatorial explosion" effect – i.e. the number of possible combinations increases rapidly as you increase the rate, and becomes huge for higher rates. By default no more than 5000 combinations are shown (there will be a button to show the rest if you need them).

One way to make this more manageable is to limit the number of examples of one value that can be used, so that you don't end up with a huge number of highly unlikely combinations involving lots of low values. If you type a number in the "Max. of one value" box, that will be taken into account. Since a franking consisting of all one value, however low, is not too unlikely there's also a "Allow single value combinations?" checkbox which will make this small exception if you set a maximum.

Getting a ½ Character

Any way that you can type ½ is OK. ALT 0189 – i.e. hold down the ALT key on the keyboard and press 0,1,8,9 on the numeric keypad – typically works, and on Windows ALT 171 will usually work as well, or a utility such as PopChar.

The simplest way is probably to use the small button marked "½" between the "Rate" and "Calculate using these values" boxes. If one of those is in focus (i.e. the cursor appears there and you can type in it) then clicking the "½" button will insert a ½ character for you.