360° Full-Circle Protractor
Measure reflex angles (180° to 360°), circular geometry, navigation bearings, and 4-quadrant trigonometry directly on uploaded images or diagrams.
Settings & Controls
Background Media
Measure angles on images, video files (MP4/WebM), or live camera feed.
Angle Measurements
0No angles marked
Click on the protractor arc to place angle markers
Live Trigonometry & Geometry HubReal-Time
Instant trigonometric ratios & circle sector metrics for active angle 0.0°
Multi-Angle Saved Measurements Log
Pin and record multiple angles from the same diagram or image.
How to Use the 360° Protractor
Measure reflex angles, bearings, and circular segments in four straightforward steps.
Set center & baseline
Drag the center crosshair to your angle's vertex (or the center of your circular figure). Rotate the baseline handle so 0° aligns with your reference line or North.
Add rays anywhere on the circle
Click anywhere along the full 360° track to place numbered pins. You can place pins across any quadrant (0° to 360°) to measure multiple sectors.
Check reflex angles & bearings
For angles over 180°, the dashboard automatically calculates the reflex angle (180°–360°) as well as the inner conjugate angle (360° − θ).
Save sectors & export
Save active sectors to your measurement log, download annotated high-resolution images, or export a CSV table for coursework or design projects.
Types of Angles & Relationships
A quick reference for angle classifications, ranges, and geometric properties.
Acute Angle
An angle strictly between 0° and 90°. Common examples include roof pitches, equilateral triangle corners (60°), and scissor blades.
Right Angle
An angle of exactly 90° (π/2 radians), forming perpendicular lines found in door frames, books, and square corners.
Obtuse Angle
An angle greater than 90° but less than 180°. Found in reclined seats, wide roof gables, and hockey stick shafts.
Straight Angle
An angle of exactly 180° (π radians). The two arms point in opposite directions to form a continuous straight line.
Reflex Angle
An angle strictly greater than 180° and less than 360°. Represents the major outer arc measured by a 360° full-circle protractor.
Complete Angle (360°)
A full 360° rotation where the ray circles completely back to the baseline (equal to 1 full turn or 2π radians).
Angle Pairs
• Complementary: Two angles that add up to 90°.
• Supplementary: Two angles that add up to 180°.
Conjugate Angles
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°).
Test & Sharpen Your Angle Skills.
A random angle diagram is generated below. Estimate the degree measure, test your geometry intuition, and click Reveal Answer!
Frequently Asked Questions
Helpful answers on how to use the online protractor, read dual scales, and export measurements.
How do I measure an angle using this online protractor?↓
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.
How do I avoid reading the wrong scale (inner vs. outer)?↓
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°.
Can I measure angles using my phone camera or uploaded photos?↓
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.
When should I use the 360° protractor instead of the 180° version?↓
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.
How do 15° magnetic snapping and keyboard nudging work?↓
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.
What does the Loupe magnifying tool do?↓
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.
Can I measure line length and angle at the same time?↓
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.
What are complementary and supplementary angle sectors?↓
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.
Will my measurements be saved if I refresh the page?↓
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.
How do I export my measurements or save a worksheet?↓
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.
Is freeProtractor completely free and private?↓
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.