Tally marks explained: how to write and read them

What tally marks are

A tally mark is a single stroke that stands for one counted thing. Tallying is what is called unary counting: the notation has one symbol, and the number is however many of that symbol you have written. It is the oldest counting notation there is, older than written numerals, and it survives because it solves a problem numerals do not.

That problem is counting while events are arriving. To write “17” you first have to know the total is 17, which means holding the running count in your head. To add a tally mark you only have to make one stroke. The paper holds the total, not you.

Because every stroke is worth one wherever it sits, tally marks are not base 5, although they are often described that way: the groups of five are a reading aid, not place values. The tally counter’s section on tally charts sets the two side by side.

How to write tally marks

1. Draw one vertical stroke for the first count.
2. Add a second, third and fourth stroke beside it, keeping them roughly parallel and evenly spaced.
3. For the fifth, draw a single diagonal line across all four.
4. Start a new group for the sixth, leaving a clear gap between groups.

To read the result, count the completed groups, multiply by five, then add the loose strokes. Three groups and two strokes is 3 × 5 + 2 = 17.

The completed group of five is called a five-bar gate in British and Irish usage, because four uprights crossed by a diagonal looks like a farm gate.

Why groups of five

Three reasons, and they compound.

• Five matches one hand. The convention almost certainly comes from finger counting, which is why base-five and base-ten grouping appear independently across unrelated cultures.
• Four is the limit of instant recognition. People can perceive up to about four items at a glance without counting, a phenomenon called subitising. Groups of five sit just past that limit but are made recognisable by the crossing stroke, which turns the group into a single shape.
• It makes errors local. If you miscount inside one group, the error is at most four. With a long unbroken run of strokes, a single miscount corrupts the entire total.

Tally marks to numbers

Tally marks examples, read step by step

Reading a tally is always the same two-step sum: count the completed groups and multiply by five, then add the loose strokes. Written out on real examples it looks like this.

The multiplication is the whole trick, and it is why the grouping exists. Nobody counts seventeen separate strokes reliably; almost everybody can count three gates and two leftovers.

Three mistakes that produce a wrong total

• Counting the diagonal as a sixth stroke. A completed gate is five, not six. The diagonal is the fifth mark, not an extra one on top of four.
• Leaving no gap between groups. Run two gates together and they read as one shape. Leave clear space, and the groups stay countable at a glance.
• Crossing at four. The diagonal goes on when you reach five, across the four already there. Crossing after three or after five is the commonest way a tally drifts.

Tally charts and frequency tables

In school maths, tally marks almost never appear on their own. They appear inside a tally chart: a list of categories with a tally beside each one, filled in as the data arrives. The chart is the recording stage, and it is deliberately the fastest thing to write while counting is happening.

A frequency table is the same chart with the tallies converted to numbers. Frequency simply means how many times something occurred, so the frequency column is the tally read as a number — which is exactly the sum from the section above.

Two things are worth noticing about that table, because both are marked in exams.

• The total row is a check, not decoration. The frequencies must add up to the number of things counted. Thirty pupils, thirty in the total. If it comes to 29 or 31, a tally was misread or a mark was missed, and you know before you draw anything.
• Every item goes in exactly one row. Categories must not overlap, or the same pupil is counted twice and the total stops being a check.

From a frequency table the rest follows: the tallest bar on a bar chart is the largest frequency, the mode is the category with the largest frequency, and the range and mean are worked out from the frequency column rather than from the strokes.

Check yourself

Read each tally before looking at the number beside it.

The second row is the one people get wrong. Four uprights with no diagonal is four, not five: the gate is only complete once the fifth mark crosses it.

Big numbers: how to write 50, 100 and more in tally marks

A tally has no symbol bigger than the gate, so 100 in tally marks is twenty gates: one hundred strokes. Nothing about the notation changes as the count grows; what changes is whether anyone can still read it. Twenty gates in one long line are as hard to count as seventeen loose strokes were, and the fix is the same idea one level up: group the groups.

The usual way is two gates to a row, so every full row is ten. Reading a big tally then becomes three steps: count the full rows and multiply by ten, add five for a gate left over, then add the loose strokes.

Two habits keep a big tally honest. Start a new row only when the old one holds two gates, so a short row can only ever be the last one; and check the total against something independent, the number of forms collected or people through the door, because a hundred strokes is a hundred chances to miss one. Past a few dozen per category, a tally on paper is the slowest and least checkable way to keep the count: that is where a counter that shows the number, and takes a mistake back cleanly, earns its place.

How other countries write them

The five-bar gate is not universal. Several other conventions are in everyday use:

• Box and diagonal, used in France, Spain, Portugal and the countries they colonised, Latin America included, where it keeps the score in card games such as truco: four strokes forming a square, with the fifth as a diagonal inside it.
• The character 正, used in China, Japan, Korea and Taiwan. It has exactly five strokes, and it is built one stroke at a time in a fixed order, so a partly written 正 shows the count within the group.
• Dot and line tallies, used in forestry: dots at the corners of a square for one to four, lines joining them for five to eight, and the two diagonals for nine and ten, so a group holds ten rather than five. The method is named after the statistician John Tukey, but MathsIsFun traces it to the forester Carl Schenck, who used it to count logs in 1898.

All of them do the same job. If you are recording data that someone else will read, use whichever convention your reader expects, and label the sheet. To type tally marks rather than draw them, Unicode has characters for one and five only, and few fonts include them; the tally mark symbols table lists the code points and the fallbacks that display everywhere. Sources for the variants: Wikipedia, Tally marks and MathsIsFun, Tukey tallying, read 2026-10-19.

Tally marks as a number system

A number system, or numeration system, needs two things: a set of symbols and a rule for combining them. Tallying is the simplest one there is. It has one symbol, the stroke, and one rule: add them up. Mathematicians call that a unary system, and textbooks on numeration start with it because every later system is an answer to its one weakness: the bigger the number, the more you have to write.

Set beside the systems that followed, the difference is plain to count:

That table is why the five-bar gate is a grouping and not a base. In base 5, the position of a symbol would change its value; in a tally, a stroke is worth one wherever it sits, and the diagonal is a stroke like the others. Grouping is the step every additive system took next: Egyptian scribes gave ten its own sign rather than ten strokes, and the gate does the same job for the eye without changing a single value.

Are Roman numerals tally marks?

I, II and III look like tallies, and many people take the rest of the system to have grown from them. Wikipedia’s article on tally marks says so directly: it lists Roman numerals, the Brahmi numerals, the Chinese numerals for one to three (一 二 三) and rod numerals as derived from tally marks. Its article on Roman numerals is more careful: the Roman symbols came “directly” from the Etruscan number symbols, and because so few examples survive, “the origins of the system are obscure and there are several competing theories, all largely conjectural.” The safe statement is the narrow one: the strokes for one to three are tallies in every system that has them, and how far the resemblance goes beyond three is not settled. The additive habit survives, too: clock faces still often show four as IIII, the way a tally would, rather than IV.

Sources: University of Houston, Math 2303, Systems of Numeration and Additive Systems of Numeration; Wikipedia, Tally marks; Wikipedia, Roman numerals; read 2026-10-19.

Where tally marks come from

Tally marks are older than writing. The oldest objects that look like tallies are notched bones: the Wolf bone, found in what is now the Czech Republic and about 30,000 years old, carries 55 marks that may be a tally, and the Ishango bone from central Africa is more than 20,000 years old (Wikipedia, Tally marks). Whether those particular notches count anything is debated. That people went on to count with notches is not.

Tally sticks: a receipt that could not be altered

For most of recorded history a tally was a notched stick, and the word comes from it. English tally descends through Anglo-Norman tallie and Medieval Latin tallia from Latin talea, “a cutting, rod, stick” (Wiktionary).

The split tally recorded a debt. Notches were cut across a stick, and the stick was split lengthwise through them. The longer half, the stock, went to whoever had advanced the money; the shorter half, the foil, went to whoever had received it (Wikipedia, Tally stick). Both halves carried the same notches, so fitting them together proved the amount, and a notch added to one half alone would not match the other.

The English Exchequer kept its accounts this way for centuries, with the width of each notch standing for an amount. The account Wikipedia quotes gives these sizes:

The tally sticks that burned down Parliament

Split tallies stayed in use at the Exchequer until 1826. In October 1834 the stock of old sticks was burned in the two furnaces under the House of Lords. The furnaces were built for coal, which burns with little flame; the wood burned with a great deal, the flues overheated, and on 16 October 1834 the fire spread and destroyed most of the Palace of Westminster. Westminster Hall survived, and the Houses of Parliament standing today were built to replace what burned (Wikipedia, Burning of Parliament).

The same habit of cutting notches gave English another counting word. Score relates to Old Norse skor, a notch, in the way tally relates to a cut stick, so keeping score and keeping a tally began as the same act.

When to tally and when not to

Tallying is the right tool when events arrive faster than you can write numbers, when you need several counts running at once, or when you must keep your eyes on what you are counting rather than on the page. Surveys, wildlife counts, traffic studies, stock takes and classroom observation all fit.

It is the wrong tool when totals go into the hundreds, when the count needs correcting often, or when the data has to end up in a spreadsheet anyway. Paper tallies cannot be undone, only crossed out, and a crossed-out tally sheet is where recount errors come from. That is the one place a digital tally counter genuinely beats paper: pressing undo takes a mark back cleanly, and the total is already a number you can copy.