Online protractor
Reflex angle 310°
Acute
The photo stays on your device. It's opened in this page and never uploaded.
Drag the numbered handles to aim the arms, the centre to move everything, and the small handle on the rim to turn the protractor. With the keyboard, Tab to a handle and use the arrow keys: one degree a press, ten with Shift.
Make it true size on this screen
A screen's pixels aren't a fixed size, so the protractor can't know how big a centimetre is until you show it. Hold a bank card or any ID card of the standard size against the screen and drag the slider until the outline matches the card's long edge. Those cards are 85.60 mm by 53.98 mm. A ruler works too: match the bar underneath to 5 cm.
Measuring on screen
Drag the centre onto the corner you want to measure, then drag handle 1 along one side of the angle and handle 2 along the other. The angle between them shows in large type as you move, with the reflex angle on the other side underneath. The two always add up to 360°.
To measure something in a picture, press Measure on a photo and choose one from your phone or computer. It opens inside this page. Nothing is sent anywhere, and closing the tab forgets it.
The drawn protractor is there to learn from. Turn it with the small handle on its rim, or press Line up with arm 1, and the panel says where each arm crosses the inner and outer scales, so you can check which one you'd have read on paper.
A screen can't be trusted for size. The same picture is a different width on a phone, a laptop and a projector, so the protractor is only true size after you calibrate it against a bank card or a ruler. Angles don't need that. A 40° corner is 40° at any size.
Printable protractor
2 × 180° protractor, 7.5 cm radius (15 cm across), on US Letter, with a millimetre ruler
Printable protractorstringmash.com/protractor
Printing it the right size
Pick a half or full circle, a size and your paper, then press Print chart. The protractor is drawn in millimetres, so a 7.5 cm radius prints 7.5 cm, but only if the printer leaves it alone. In the print dialog set the scale to 100% or Actual size, never Fit to page.
Then check it. Across the top of the sheet is a line that should measure exactly 100 mm. Put a ruler on it. If it comes out short, the printer shrank the page and every degree mark has moved with it.
For a protractor that lasts, print onto card, or onto an overhead transparency so you can see the lines through it. Tick Cutting line for a dashed line 3 mm outside the edge to cut along. Download SVG saves the same sheet to print from another program at its true size.
How to measure an angle with a protractor
Put the centre mark exactly on the vertex, the point where the two lines meet. Turn the protractor until its baseline lies along one arm of the angle. Then follow the scale that reads 0 on that arm round to where the other arm crosses the edge, and read the number there.
Every protractor has two rows of numbers running opposite ways, so that you can measure an angle opening either way. If the arm along the baseline points right, the inner scale starts at 0 there. If it points left, use the outer scale. The Open University's worked example is an angle of 40° that's easy to misread as 140° from the wrong row.
Estimate first. If the angle is plainly narrower than a corner of a page, the answer is under 90°, and a reading of 140° means you've used the wrong scale.
A half-circle protractor stops at 180°. For a reflex angle, measure the smaller angle on the inside and take it from 360°. If the inside reads 140°, the reflex angle is 220°. A full-circle protractor reads it directly.
Protractors measure in degrees. To turn a reading into radians, use degrees to radians, and the unit circle puts the common angles in both units on one chart.
How to draw an angle
Rule a straight line for the first arm and mark the vertex at one end. Lay the protractor with its centre on the vertex and the baseline along the line. Count up from the 0 that sits on your line to the angle you want and make a small dot at that mark.
Lift the protractor off and rule a line from the vertex through the dot. Measure the finished angle to check it.
Types of angle
| Name | Size | What it looks like |
|---|---|---|
| Zero angle | 0° | Both arms on top of each other |
| Acute angle | More than 0°, less than 90° | Sharper than the corner of a page |
| Right angle | 90° | A square corner, a quarter turn. Often marked with a small square. |
| Obtuse angle | More than 90°, less than 180° | Wider than a square corner but not flat |
| Straight angle | 180° | A straight line, a half turn |
| Reflex angle | More than 180°, less than 360° | The outside of a corner, the long way round |
| Full angle | 360° | One whole turn, back where you started |
Questions
Why did my printed protractor come out the wrong size?
The print was scaled. Open the print dialog again, set the scale to 100% or Actual size, and make sure the paper size matches the one picked here. The 100 mm line at the top tells you whether it worked.
Which scale do I read, inner or outer?
The one that reads 0 on the arm lying along the baseline. If that arm points right, read the inner numbers; if it points left, read the outer ones. A quick estimate catches mistakes: an angle that looks sharp can't be 140°.
How do I measure an angle bigger than 180°?
Measure the smaller angle on the other side and subtract it from 360°. Or print the 360° protractor, which reads all the way round.
Is the online protractor accurate?
The angle is worked out from where the handles are, to the nearest degree, so it's as accurate as you can place them. Zoom in on a photo, or use the arrow keys for one degree at a time. Size on screen is only true after you calibrate.
How does the calibration work?
Bank cards and most ID cards are made to one standard size, ID-1 in ISO/IEC 7810, which is 85.60 mm by 53.98 mm. When the outline on screen matches a real card, the page knows how many pixels make a millimetre on your screen and draws a 7.5 cm protractor at that scale. It remembers the setting in this browser only.
Is my photo uploaded?
No. It's read from your device inside the page and drawn under the protractor. It never leaves your computer or phone, and it's gone when you close the tab.
Sources
- Wikipedia: Protractor
- Wikipedia: Angle (types of angle)
- Wikipedia: ISO/IEC 7810 (ID-1 card size)
- The Open University, OpenLearn: How to measure an angle
- CIMT, Mathematics Enhancement Programme, Book 7 Unit 5.2: Measuring angles
- Inch Calculator: How to use a protractor
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