Measure angles directly on photos, technical drawings, or your camera feed. Switch between 180° and 360°, log multiple points, and export your calculations.
Measure angles on images, video files (MP4/WebM), or live camera feed.
No angles marked
Click on the protractor arc to place angle markers
Instant trigonometric ratios & circle sector metrics for active angle 0.0°
Pin and record multiple angles from the same diagram or image.
Whether measuring a photo, technical blueprint, or live camera feed, here is the exact process.
Drag and drop an image (PNG, JPG, WebP), click Upload Image, or launch your webcam to measure real physical objects directly on your screen.
Choose the classic 180° Semicircle for standard triangles and roof angles, or the 360° Circle for reflex angles (>180°), pie charts, and compass bearings.
Drag the center handle onto the corner (vertex). Rotate the baseline arm until the 0° line aligns with the first side of the angle.
Drag the measurement ray to the second arm. Read degrees (°), radians (rad), and trigonometry ratios (sin, cos, tan). Save to table or export worksheet.
A quick reference for angle classifications, ranges, and geometric properties.
An angle strictly between 0° and 90°. Common examples include roof pitches, equilateral triangle corners (60°), and scissor blades.
An angle of exactly 90° (π/2 radians), forming perpendicular lines found in door frames, books, and square corners.
An angle greater than 90° but less than 180°. Found in reclined seats, wide roof gables, and hockey stick shafts.
An angle of exactly 180° (π radians). The two arms point in opposite directions to form a continuous straight line.
An angle strictly greater than 180° and less than 360°. Represents the major outer arc measured by a 360° full-circle protractor.
A full 360° rotation where the ray circles completely back to the baseline (equal to 1 full turn or 2π radians).
• Complementary: Two angles that add up to 90°.
• Supplementary: Two angles that add up to 180°.
Two angles that add up to 360° (a + b = 360°). Divided into four 90° quadrants: Q I (0–90°), Q II (90–180°), Q III (180–270°), and Q IV (270–360°).
Standard geometric angles with exact radian equivalents, sine, cosine, tangent ratios, and everyday examples.
| Degrees | Radians (Exact) | Radians (Dec) | sin(θ) | cos(θ) | tan(θ) | Category | Real-World Application |
|---|---|---|---|---|---|---|---|
| 0° | 0 | 0.000 | 0 | 1 | 0 | Zero | Flat baseline, horizontal reference, level ground |
| 30° | π/6 | 0.524 | 1/2 (0.5) | √3/2 (~0.866) | √3/3 (~0.577) | Acute | 30-60-90 drafting triangle, clock hand at 1:00 |
| 45° | π/4 | 0.785 | √2/2 (~0.707) | √2/2 (~0.707) | 1.0 | Acute | Standard miter saw cut, 45-45-90 triangle, 100% grade |
| 60° | π/3 | 1.047 | √3/2 (~0.866) | 1/2 (0.5) | √3 (~1.732) | Acute | Equilateral triangle internal angle, honeycomb hexagon |
| 90° | π/2 | 1.571 | 1 | 0 | Undefined (∞) | Right | Square corner, perpendicular lines, book corner, clock at 3:00 |
| 120° | 2π/3 | 2.094 | √3/2 (~0.866) | -1/2 (-0.5) | -√3 (~-1.732) | Obtuse | Regular hexagon interior angle, 3-phase electric power |
| 135° | 3π/4 | 2.356 | √2/2 (~0.707) | -√2/2 (~-0.707) | -1.0 | Obtuse | Octagon internal angle (stop sign), bay window angle |
| 150° | 5π/6 | 2.618 | 1/2 (0.5) | -√3/2 (~-0.866) | -√3/3 (~-0.577) | Obtuse | Clock hand at 5:00, wide roof gable pitch |
| 180° | π | 3.142 | 0 | -1 | 0 | Straight | Continuous straight line, semicircle rim, clock at 6:00 |
| 270° | 3π/2 | 4.712 | -1 | 0 | Undefined (∞) | Reflex | Three-quarter turn, south on compass bearing, clock at 9:00 |
| 360° | 2π | 6.283 | 0 | 1 | 0 | Full Circle | Full 360° rotation, complete circumference, compass 000°/360° |
Example: 90° × (π / 180) = π/2 ≈ 1.5708 radians.
Example: 1 radian ≈ 57.2958 degrees.
Example: 45° angle has tan(45°) = 1.0 = 100% slope grade.
From school homework to job site inspections and clinic assessments, freeProtractor handles real measuring tasks.
Measure miter joint angles (45°), crown molding bevels, roof rafter plumb cuts, and staircase stringer pitches directly from workpiece photos before cutting expensive lumber.
Verify triangle angle-sum theorems (180°), calculate complementary & supplementary pairs, solve polygon interior angles, and demonstrate trigonometry ratios on classroom smartboards.
Check wheelchair ramp gradients against ADA standards (max 4.76° or 1:12 slope), verify roof gable pitches, inspect retaining walls, and measure blueprint elevations.
Assess patient joint flexibility, knee flexion/extension (0° to 140°), shoulder abduction, and ergonomic desk posture angles from video frames or clinic photos.
Inspect 3D print model overhang angles (avoiding >45° without supports), check mold draft angles for injection molding, and measure mechanical linkage clearance.
Calculate optimal solar panel tilt angles based on geographic latitude and seasonal solstice variations, measure sun shadow angles, and track celestial horizon arcs.
See how freeProtractor compares against traditional online protractor tools.
Snap photos directly with your phone/laptop camera or drag and drop any engineering blueprint, math worksheet, or photo to measure angles in real time.
Don't lose your measurements. Record up to 5 distinct angles simultaneously, export high-resolution PNG overlays, or download CSV data reports.
Full smooth 0.01° sub-pixel precision with optional magnetic angle snapping to 1°, 5°, 15°, or 45° standard geometric angles.
| Capability / Feature | freeProtractor.com | onlineprotractortool.com | visnos.com |
|---|---|---|---|
| Device WebCam Camera Input | ✓ Live Support | ✗ No Camera Mode | ✗ No Camera Mode |
| Multi-Angle Simultaneous Tracking | ✓ Log up to 5 angles | ✗ Single angle only | ✗ Single angle only |
| 3-Point Pin Angle Measurement Mode | ✓ Direct Pin Vertex | Basic Overlay | Basic Overlay |
| Trigonometric Readout (sin, cos, tan) | ✓ Real-time trig functions | ✗ None | ✗ None |
| Magnetic Angle Snap (1°, 5°, 15°, 45°) | ✓ Toggleable snap steps | ✗ Smooth drag only | ✗ Smooth drag only |
| CSV & PNG Export Options | ✓ PNG + CSV Data export | Basic PNG | ✗ None |
| Clean Modern Design & Zero Ads | ✓ 100% Ad-Free, Stark UI | ✗ Heavy Ads & Banners | Dated Flash Look |
A random angle diagram is generated below. Estimate the degree measure, test your geometry intuition, and click Reveal Answer!
Step-by-step tutorials to help students, DIYers, and professionals master angle measurement.
The complete, beginner-friendly handbook covering protractor anatomy, baseline alignment, reading concentric scales, and common geometric mistakes.
Never pick the wrong degree number again. Learn the baseline 0° rule and the simple 90° sanity check that eliminates scale confusion forever.
A hands-on walkthrough for measuring acute, right, obtuse, straight, and reflex angles with real-world examples and diagrams.
A fun guide using pizza slices, alligator mouths, and index-card tricks to make geometry intuitive for 3rd, 4th, and 5th graders.
Understand how protractor scales work, how to avoid common reading mistakes, and how angles connect to trigonometry.
A protractor measures the angle formed between two intersecting lines, expressed either in degrees (0° to 360°) or radians (0 to 2π). Depending on what you are measuring, you will generally choose between two standard shapes:
The classic D-shaped tool. Best for measuring flat angles, triangles, polygons, and any angle up to 180°. It is compact and easy to align with a straight baseline.
A full circular disk covering all four quadrants (0° to 360°). Essential for reflex angles (greater than 180°), compass bearings, rotational machinery, and circular charts without needing to flip the tool.
Most physical and digital protractors feature two sets of degree numbers running in opposite directions along the arc. This allows measuring angles opening to either the left or the right, but it is also the most common source of measurement errors.
Whichever arm of the angle rests flat against the baseline, find where that arm hits 0°. Follow that same scale track around to the second arm.
If the opening looks sharp and narrower than a square corner, it is acute and must be under 90°. If it is wider than a square corner, it is obtuse and must be between 90° and 180°. If your protractor reads 40° but the angle is clearly wide, you are reading the wrong scale (it should be 140°).
Measuring angles on paper with a traditional plastic protractor works well when lines are long enough to reach the outer scale. But with small textbook diagrams, phone photos, or digital blueprints, physical tools run into practical limits:
Whenever you measure an angle (θ) relative to a baseline, it directly defines the proportions of a right-angled triangle. Here is a quick reference for the core ratios:
If you are working through multiple math exercises or inspecting a part:
Helpful answers on how to use the online protractor, read dual scales, and export measurements.
Drag the center crosshair directly onto the vertex (corner) of your angle. Use the baseline handle to rotate the 0° line along one arm of the angle, then drag the active ray handle to the second arm. The angle degree, radians, and trigonometric values update in real time.
Always count up from 0° starting on the arm that lies on your baseline. As a quick sanity check: if the opening is sharper than a square corner, it is acute and must be under 90°. If it is wider than a square corner, it is obtuse and must be between 90° and 180°.
Yes. Click 'Upload Image' to measure angles directly on diagrams, blueprints, or homework screenshots. You can also click 'Use Camera' on your phone or computer webcam to measure physical objects in front of your camera.
The standard 180° semicircle is best for triangles, polygons, and typical math problems. Switch to the 360° full circle when you need to measure reflex angles (180° to 360°), circular pie charts, mechanical gears, or compass bearings.
Turn on 'Snap' to magnetically lock onto common milestone angles like 30°, 45°, 60°, and 90°. You can also use your keyboard Left / Right arrow keys to nudge the active ray by 1.0°, or hold Shift + Arrow for fine 0.1° adjustments.
When the Loupe toggle is active, dragging the center point or ray pins automatically brings up a 2.5x circular zoom window over your cursor. This makes it easy to target thin lines and fine vertices on high-detail drawings.
Yes. Click 'Ruler' to display centimeter and inch graduations along the baseline ray, allowing you to check line segment length and angle simultaneously without switching tools.
Toggling 'Comp' highlights the angle's complementary sector (what is needed to reach 90°) and supplementary sector (what is needed to reach 180°) with distinct colors and live degree badges.
Yes. All marked rays, protractor position, radius scale, and theme preferences are automatically saved in your browser's local storage. If you refresh or close the tab, your session is restored.
Click 'Save Angle' (or press S) to record measurements in the table below the canvas. You can download the log as CSV, Excel, or JSON, or click 'Export PDF / PNG' to download a clean annotated worksheet image.
Yes, it is 100% free with no account or installation required. All calculations, images, and camera feeds stay strictly inside your browser and are never uploaded to our servers.
