Number Line Generator
Printable number lines with fractions, jumps and inequalities, as PNG, SVG or PDF.
Your number line
This is the last number line drawn. Fix the input to update it.
| Typed | Interval | Inequality | Set-builder |
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About the Number Line Generator
Draw a number line for any range — whole numbers, negatives, decimals or fractions — and mark it up: points with names, addition and subtraction jumps (or multiplication as repeated jumps), and inequalities or intervals with open and closed dots. The picture redraws as you type, and the values are exact: a tick at 1/3 sits exactly a third of the way along, and 0.1 + 0.2 lands on 0.3.
Labels can be decimals, fractions or mixed numbers, simplified or kept over one denominator (2/4, 3/4, 4/4) for teaching equivalent fractions, or left blank for a worksheet. Every inequality is also written out in interval, inequality and set-builder notation.
Download the line as a PNG for slides, an SVG for documents, or a PDF with up to ten copies on a page for worksheets. Nothing is uploaded.
How to use it
- Type the Start, the End and the distance between labelled ticks (Tick every), such as −10, 10 and 1, or 0, 2 and 1/4. Choose Minor ticks if you want halves, quarters or tenths between them without labels.
- Choose how labels are written — decimals, fractions or mixed numbers — and which ticks get one. Untick Simplify fractions to keep every label over the same denominator, or choose No labels for a blank line.
- Under On the line, type points (
3/4, −2.5, A = 1.5), a sum of jumps (3 + 4 − 2), or inequalities and intervals, one per line (x > 2,−1 ≤ x < 3,(−∞, 4]). - Check the preview, then press PNG, SVG or PDF. For a worksheet, pick how many copies go on the PDF page and tick Name line; Print prints the number line with its description and notation, without the form.
Examples
Start −10 · End 10 · Tick every 1
21 labelled ticks with arrows at both ends; 0 is in bold
On a narrow phone screen only every 5th label is shown so that none overlap; the downloads are always full size.
Start 0 · End 1 · Tick every 1/3 · Fractions · Simplify off
0/3, 1/3, 2/3, 3/3
Jumps: 3 + 4 − 2
An arc from 3 to 7 labelled +4, then one back to 5 labelled −2; the result line reads 3 + 4 − 2 = 5
Jumps: 12 ÷ 5
Two jumps of −5 from 12, stopping at 2: 12 ÷ 5 = 2 remainder 2
x ≤ −2 or x > 4
A closed dot at −2 with an arrow to the left, an open dot at 4 with an arrow to the right; interval notation (−∞, −2] ∪ (4, ∞)
Common uses
- Worksheets: a page of blank or partly labelled lines for “fill in the missing numbers” or “plot these fractions”.
- Showing addition and subtraction as jumps, or multiplication as repeated jumps, in a lesson or on a slide.
- Graphing the solution of an inequality — and checking its interval notation — for algebra homework.
- Fractions and decimals: comparing 3/4 and 0.7, or seeing that 2/4 and 1/2 are the same point.
- Temperatures, timelines and other scales that run below zero.
Open and closed dots, brackets and arrows
A closed (filled) dot means the number itself is included: it goes with ≤ and ≥, and with a square bracket in interval notation, as in [−1, 3). An open (hollow) dot means the number is left out: it goes with < and >, and with a round bracket. An arrow at the end of the shading means the set goes on for ever in that direction; infinity is never included, so ∞ always takes a round bracket.
x > 2— open dot at 2, shading to the right: (2, ∞)x ≤ −1— closed dot at −1, shading to the left: (−∞, −1]−1 ≤ x < 3— closed dot at −1, open dot at 3, shading between: [−1, 3)x < 0 or x ≥ 4— two pieces: (−∞, 0) ∪ [4, ∞)x ≠ 0— the whole line except an open dot at 0: (−∞, 0) ∪ (0, ∞)
You can type either form. Overlapping or touching intervals are joined, so [1, 3] ∪ [2, 5) is drawn and written as [1, 5).
Jumps
- Addition and subtraction: the first number is the start and each
+or−is one jump:3 + 4 − 2starts at 3, jumps 4 to the right and 2 back. Negative starts and jumps work too:−5 + 8,3 + −2. - Multiplication:
4 × 3makes four jumps of 3 from 0 (the first number counts the jumps), ending at 12. - Division:
12 ÷ 3(or12 : 3) jumps back from 12 in steps of 3 until it reaches 0 — four jumps — and12 ÷ 5stops when less than 5 is left, at the remainder 2. - Hops of one tick: tick Show each jump as hops of one tick to draw +4 as four hops of +1, for counting on.
Each arc’s height follows the length of its jump, so a jump back inside an earlier one sits under it, and an arc is raised when it would run through another jump’s label. When points or extra rows of inequalities lie between the jumps and the line, dotted lines show where each jump starts and lands.
Fractions and decimals
With Automatic labels the line uses fractions when you typed a fraction (1/4) or chose a step whose decimal never ends (1/3), mixed numbers when you typed one (1 1/2), and decimals otherwise. Stacked fractions are drawn with a fraction bar, as in a textbook.
A decimal label is exact when the decimal ends (1/8 is 0.125) and rounded to two places when it does not (1/3 is shown as 0.33, and the page says so). With Simplify fractions off, labels share the denominator of the ticks: on a line in quarters, 1/2 is written 2/4 and 1 is 4/4.
Decimals are written with a point or a comma (2.5 or 2,5), as is usual in your country, until you choose under Title and look. With a decimal comma, separate points with semicolons (A = 1,5; 2,25) and the two ends of an interval with a semicolon: [−2; 3).
Downloads and printing
The PNG is 2,400 pixels wide on a white background, sharp enough for slides and printing; the SVG is a vector file for Word, Google Docs, PowerPoint or an image editor. The PDF is vector too, on A4 or US Letter: one or two copies of the line on a landscape page, or three to ten on a portrait page as a worksheet, with an optional name line. Black and white turns the coloured points, jumps and shading into black and grey for photocopying. All of them are made in your browser.
Limitations
- Up to 201 major ticks (−100 to 100 in ones) and 1,000 ticks in all, 30 points, 60 jumps and 4 inequalities or intervals on one line. With many ticks, labels move to every 2nd, 5th or 10th tick so they do not overlap. Hops of one tick are drawn for up to 120 hops; beyond that each jump is drawn as one arc.
- Numbers can be whole numbers, decimals, fractions and mixed numbers. Irrational numbers such as π or √2 are not accepted — type a decimal approximation such as 3.14.
- One variable per line of inequalities, and no absolute values (|x| < 3): write that one as −3 < x < 3.
- The PDF uses the standard Helvetica and Symbol fonts, so letters outside the Latin alphabet in a title or point name are printed as “?” (the page tells you which); the PNG and SVG downloads use your device’s fonts and show them.
Privacy
Everything is drawn in your browser and nothing you type is uploaded. Your last number line and paper size are kept in this browser’s storage, so they are still there next time.
Frequently asked questions
How do I make a number line with fractions?
Set the Tick every box to the fraction you want, such as 1/4 for quarters or 1/3 for thirds, and the labels switch to fractions. Choose Mixed numbers to write 5/4 as 1 1/4, and untick Simplify fractions to label every tick over the same denominator (0/4, 1/4, 2/4, 3/4, 4/4).
How do I show an inequality on a number line?
Type it in Inequalities and intervals, for example x > 2 or −1 <= x < 3. The line gets an open dot for < and >, a closed dot for ≤ and ≥, shading between the ends and an arrow where it goes on for ever. The table under the line gives the same set in interval notation (2, ∞) and set-builder notation {x | x > 2}.
What is the difference between an open and a closed circle?
A closed (filled) circle means the number is part of the answer, as in x ≥ 2; an open (hollow) circle means it is not, as in x > 2. In interval notation they are a square bracket [2, ∞) and a round bracket (2, ∞).
Can I make a blank number line for a worksheet?
Yes. Choose No labels (blank) — or Only the two ends for a “fill in the missing numbers” sheet — then press PDF with several copies on the page and tick Name line. The “Blank 0–20 worksheet” example sets this up.
How do I show 3 + 4 − 2 on a number line?
Type 3 + 4 − 2 in Jumps. The line starts at 3, jumps 4 to the right to 7 and 2 back to 5, and shows 3 + 4 − 2 = 5. Tick Show each jump as hops of one tick to count on in ones.
Why are some labels missing?
When the ticks are too close for every label to fit — a long range on a phone, or −50 to 50 in ones — labels are shown on every 2nd, 5th or 10th tick, always including 0, and the page says so. Widen the window, use a larger tick interval or a shorter range to label them all; the PNG, SVG and PDF are drawn wider than the screen and fit more.