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freeProtractor

360° Full Circle Online Protractor.

Measure reflex angles (180° to 360°), circular geometry, navigation bearings, and 4-quadrant trigonometry directly on uploaded images or diagrams.

📱Touch protractor center/arms to measure • Scroll page outside canvas
Active Angle
0.0°
Click Arc to MarkMarks: 0
R:240px
Rot: 0.0°
📐

Live Trigonometry & Geometry HubReal-Time

Instant trigonometric ratios & circle sector metrics for active angle 0.0°

Sine (sin θ)0.0000
Cosine (cos θ)1.0000
Tangent (tan θ)0.0000
Cosecant (csc θ)Undefined
Secant (sec θ)1.0000
Cotangent (cot θ)Undefined
Arc Length (s)0.0 px
Sector Area (A)0.0 px²
Ruler Length (cm)6.35 cm
Ruler Length (in)2.50 in
Radians (rad)0.000 rad
Complement (90°-θ)90.0°
Supplement (180°-θ)180.0°
Explement (360°-θ)360.0°

Settings & Controls

Background Media

Measure angles on images, video files (MP4/WebM), or live camera feed.

Angle Measurements

0
Measure Angle Between Any 2 Points
Direct Span
Angle ∠(1, 2)Radians: 0.000 rad
0.00°
+

No angles marked

Click on the protractor arc to place angle markers

Export Data
⌨️

Keyboard Shortcuts & Nudge

Nudge active ray angle ±1.0°
Shift+
Precision micro-nudge ±0.1°
Grow / Shrink Protractor radius
SpacePin new measurement ray
SSave current angle to log table
?/H
Toggle shortcuts helper modal

Multi-Angle Saved Measurements Log

Pin and record multiple angles from the same diagram or image.

#Angle (°)ClassificationRadiansTime RecordedAction
No saved measurements yet. Click "Save Angle" on the tool above to record multiple angles.
🧭 Step-by-Step Guide

How to Use the 360° Protractor.

Follow these 4 simple steps to measure reflex angles, navigation bearings, and circular diagrams online.

01

Align Center Vertex & Baseline

Drag the protractor center directly over the angle vertex or center of your image. Rotate the protractor so 0° aligns with your baseline or True North.

02

Pin Rays Across All 4 Quadrants

Click anywhere on the full 360° circular track to place numbered ray pins. Place pins in Q I, Q II, Q III, or Q IV to measure any angle from 0° to 360°.

03

Read Reflex & Explementary Angles

For angles >180°, the dashboard automatically classifies the reflex angle (180°–360°) and computes the inner conjugate angle (360° − θ) with floating badges.

04

Log Multi-Slices & Export PNG/CSV

Click 'Save Angle' to log each sector into your table. Export annotated high-res PNG images or download CSV spreadsheet reports for your coursework or CAD designs.

📐 Geometry Knowledge Base

Understanding Angles & Relationships.

Master the geometric properties of angles, unit conversions, and real-world applications.

0° < θ < 90°Acute

Acute Angle

An angle that measures strictly between 0° and 90°. Examples include 30° roof pitches, scissor openings, and 60° equilateral triangles.

Trig: sin(θ) > 0, cos(θ) > 0
θ = 90°90° Perpendicular

Right Angle

An angle of exactly 90° (π/2 radians), forming a quarter circle. Found in square corners, picture frames, and perpendicular street grids.

Trig: sin(90°) = 1.0, cos(90°) = 0
90° < θ < 180°Obtuse

Obtuse Angle

An angle that measures greater than 90° but less than 180°. Found in reclined chairs, wide roof gables, and clock hands at 4:00.

Trig: sin(θ) > 0, cos(θ) < 0
θ = 180°180° Flat

Straight Angle

An angle of exactly 180° (π radians), forming a flat straight line. Represents half of a complete rotation.

Trig: sin(180°) = 0, cos(180°) = -1.0
180° < θ < 360°Reflex

Reflex Angle

An angle strictly greater than 180° and less than 360°. Represents the major outer arc measured by a 360° full-circle protractor.

Outer Arc = 360° − Inner Angle
θ = 360° (2π rad)Full Circle

Complete Angle (360°)

A full 360° rotation where the ray completes a complete circle back to the 0° baseline. Forms a full turn (1.0 Turn = 400 gon = 2π rad).

Trig: sin(360°) = 0, cos(360°) = 1.0
Sum = 90° or 180°Pairs

Angle Pairs

Complementary: Sum equals 90° (a + b = 90°).
Supplementary: Sum equals 180° (a + b = 180°).

Vertical Opposite Angles: Equal (a = c)
Sum = 360° | 4 QuadrantsExplementary

360° Explementary Angles

Two angles whose sum is 360° (a + b = 360°). Divided into 4 quadrants: Q I (0–90°), Q II (90–180°), Q III (180–270°), and Q IV (270–360°).

Bearings: Measured clockwise from North
🎯 Interactive Practice Quiz Mode

Test & Sharpen Your Angle Skills.

A random angle diagram is generated below. Estimate the degree measure, test your geometry intuition, and click Reveal Answer!

Target AngleAcute Angle
Estimate the angle:Score: 0 / 0
Frequently Asked Questions

Everything You Need to Know About Protractors.

Got questions about measuring 180° and 360° angles online or on paper? Here are answers to the most common protractor queries.

How to use a protractor?

To use a protractor, place its center origin crosshair point directly over the angle's vertex (the corner point). Align the flat 0° baseline with one ray of the angle. Trace the second ray outwards to read the degree mark where it intersects the curved scale.

What is a protractor?

A protractor is a semi-circular (180°) or circular (360°) geometry measuring tool designed to measure and draw angles in degrees (°) or radians. Protractors are essential instruments in mathematics, engineering, drafting, woodworking, and navigation.

How to use a protractor to measure angles?

Align the protractor's center origin hole over the angle vertex, align the 0° line with one arm of the angle, and read the degree number along the scale where the second arm crosses the arc. On freeProtractor.com, you can also upload photos or use your camera to measure digital angles.

How to read a protractor?

Protractors feature dual concentric scales running in opposite directions (0°–180° and 180°–0°). To read a protractor accurately, always start counting from 0° on the baseline arm you aligned. If the angle opens to the right, read the inner scale; if it opens to the left, read the outer scale.

What does a protractor look like?

A physical protractor is a clear plastic D-shaped semi-circle (180°) or full circle (360°) calibrated with degree lines along its curved edge, a flat bottom baseline, and a center origin point. A digital protractor displays an identical scale on screen with interactive drag handles.

How to use a protractor for kids?

Teaching kids how to use a protractor is easy: 1) Place the center dot of the protractor right on the corner (vertex) of the angle. 2) Line up the bottom flat line with 0°. 3) Follow the second line up to read the number. Remind kids that sharp angles are acute (<90°) and wide angles are obtuse (>90°).

What is a 360 degree protractor called?

A 360 degree protractor is officially called a Full-Circle Protractor or Circular Protractor. It provides a complete 360-degree scale divided into four 90° quadrants, making it ideal for measuring reflex angles (>180°), circular pie charts, and navigation azimuth bearings.

What is a 180 degree protractor called?

A 180 degree protractor is officially called a Semi-Circular Protractor or Semicircle Protractor. It is the standard D-shaped measuring ruler used in geometry classes to measure acute (0°–90°), right (90°), and obtuse (90°–180°) angles.

Can my phone be a protractor?

Yes! Your smartphone (iOS or Android) can act as a digital protractor. Simply open freeProtractor.com in your mobile browser, take a photo or upload an image, and touch points on screen to measure exact angles without installing any app.

What is 90, 180, and 360 degrees?

In geometry: 90 degrees (90°) is a Right Angle forming a square corner. 180 degrees (180°) is a Straight Angle forming a flat straight line. 360 degrees (360°) is a Complete Angle representing one full circular turn back to the start.

Do iPhones have a protractor?

iPhones do not have a built-in standalone protractor app (though Apple's Measure app includes a spirit level). However, you can instantly use a full digital 180° and 360° protractor on any iPhone by visiting freeProtractor.com in Safari.

What if I don't have a protractor?

If you don't have a physical protractor: 1) Use an online digital protractor at freeProtractor.com by uploading a photo of your paper. 2) Print a free 1:1 scale printable PDF protractor template. 3) Fold a square piece of paper to use built-in 90° and 45° reference angles.

Can I check angles online?

Yes! You can check and measure any angle online for free at freeProtractor.com. Upload any picture, image (PNG/JPG), engineering drawing, or live camera feed to measure angles with 0.01° sub-pixel precision.

Is there a circle protractor?

Yes! A circle protractor (or 360° full-circle protractor) is a round measuring tool that covers a complete 360° rotation. It allows measuring pie chart sectors, reflex angles, and rotation angles without flipping the tool over.

How to make a DIY protractor?

To make a DIY paper protractor: 1) Trace a semi-circle on paper using a round bowl. 2) Fold the semi-circle in half to mark the 90° right angle line. 3) Fold in thirds to mark 30° and 60°. 4) Draw line rays from the center origin to each fold and label the degree numbers from 0° to 180°.