freeProtractor logo
freeProtractor

The Precision Online Digital Protractor.

Measure any angle on photos, engineering diagrams, or live video feeds. Sub-pixel 0.01° accuracy with instant trigonometric conversions.

Open Protractor ToolHow to Use
📱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
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

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.
📐 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
📖 Ultimate Geometry & Trigonometry Guide

The Ultimate Guide to the Protractor & Angle Measurement.

Everything you need to know about what a protractor is, how to use a protractor to measure angles, digital vs printable protractor tools, and advanced trigonometry angle calculations.

1. What is a Protractor? (Protractor Definition)

A protractor is a fundamental geometry measuring tool designed to determine the size of an angle in degrees (°) or radians. By definition, a protractor definition specifies a semi-circular or circular device calibrated with degree markings along its curved circumference. Whether you are searching for a physical ruler, a printable protractor, or a browser-based online protractor, the protractor remains an essential instrument in mathematics, engineering, navigation, woodworking, and technical drafting.

Historically crafted from brass, wood, or clear acrylic plastic, modern measurement has evolved into the digital era with the digital protractor and virtual protractor tool. Using an interactive protractor online allows students, teachers, and professionals to measure angles directly on any digital protractor image or uploaded protractor png overlay without needing a physical plastic ruler.

🌓 180 Degree Protractor (Half Circle)

The classic 180 degree Protractor (also called a 180 protractor or semi-circle protractor) features a 0° to 180° scale. It is ideal for measuring acute, right, and obtuse angles in standard school geometry classes.

◯ 360 Degree Protractor (Full Circle)

A 360 degree protractor (or 360 protractor) provides a full 360° circular scale. It enables measuring reflex angles, complete rotations, navigation azimuth bearings, and mechanical engineering designs.

2. How to Use a Protractor to Measure Angles

Learning how to use a protractor is one of the foundational skills in elementary and middle school geometry. Whether working with a physical tool on paper or utilizing a digital protractor tool on screen, follow these step-by-step instructions on how to use protractor instruments correctly:

  1. Align the Center Origin (Vertex): Place the center crosshair hole (the origin point) of your geometry Protractor directly over the vertex (the corner point) where the two rays meet.
  2. Align the Baseline (0° Line): Rotate the protractor baseline so that the 0° line perfectly overlaps one of the angle’s rays (the baseline arm).
  3. Read the Scale Ray Alignment: Trace the second ray of the angle outwards until it intersects the curved degree scale of your 180 degree Protractor or 360 degree protractor.
  4. Identify Inner vs. Outer Scale: Standard protractors have two concentric sets of numbers running in opposite directions. Always start counting from 0° on your baseline ray to ensure you read the correct acute or obtuse angle value.
💡 Pro Tip for Online Protractor Users: When using our virtual protractor online, you can drag the center target to any position on your screen, drag the outer handle to rotate the scale, and toggle 15° magnetic snap for exact angle alignment on any photo or document image.

3. Digital Protractor vs. Printable Protractor & Protractor PNG

Different tasks require different types of protractor tools. Understanding when to use a printable protractor versus a web-based digital protractor helps educators, students, and engineers achieve maximum accuracy.

🖨️ Printable Protractor Sheets & Paper Templates

A printable protractor is a downloadable PDF template that students can print on paper or transparent film for classroom tests. Our tool allows exporting high-resolution 1:1 scale printable sheets.

🖼️ Transparent Protractor PNG & Protractor Image Overlays

A protractor png image with a transparent background is ideal for inserting into presentation slides, digital graphic design work, or CAD software. You can upload any protractor image or background picture directly into our interactive canvas tool.

💻 Interactive Online Digital Protractor Tool

Our online protractor software offers sub-pixel 0.01° precision, live camera measuring, multi-ray angle logging, and automatic unit conversion—features impossible with traditional physical protractors (even if searched as protrctor).

4. Geometry Protractor & Trigonometry Angle Calculations

A geometry Protractor does more than just measure flat angles in degrees—it bridges geometry with trigonometry. Calculating a Trignometry angle with protractor readouts allows instant calculation of trigonometric functions for right triangles and unit circles:

sin(θ)Opposite / Hypotenuse
cos(θ)Adjacent / Hypotenuse
tan(θ)Opposite / Adjacent
Arc Length (s)s = r · θ (rad)
Sector Area (A)A = ½ r² · θ (rad)
Complement / Supp.90°−θ | 180°−θ

Our live trigonometry engine computes $\sin(\theta)$, $\cos(\theta)$, $\tan(\theta)$, $\csc(\theta)$, $\sec(\theta)$, and $\cot(\theta)$ simultaneously as you drag protractor handles on screen, helping students solve trigonometry homework problems with zero manual formula entry.

5. Measuring Angles with a Protractor Worksheet Generator

Teachers and parents frequently search for measuring angles with a protractor worksheet assignments for student practice. With freeProtractor.com, you can create custom annotated worksheets in seconds:

  • Mark multiple angle rays across any uploaded diagram or geometric figure.
  • Click the Export PDF / PNG button in the top toolbar.
  • Add custom worksheet titles, student names, and step-by-step problem notes.
  • Generate a 1-click printable PDF report featuring high-resolution annotated protractor diagrams and exact measurement tables.

Whether practicing basic angle classification (acute, right, obtuse, reflex) or completing advanced engineering inspection logs, our online tool makes generating measuring angles with a protractor worksheet documents fast, free, and accurate.

❓ 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°.