Goniometer

A goniometer is a special tool used to measure angles or to turn an object to an exact angle. The word goniometry comes from two ancient Greek words: γωνία (gōnía) meaning 'angle' and μέτρον (métron) meaning 'measure'.

One common kind of goniometer that many people know is the protractor, which is used in subjects like mechanics, engineering, and geometry.

Goniometer made by Develey le Jeune in Lausanne, late 18th–early 19th century

The very first description of a goniometer was written by Gemma Frisius in 1538, and it was based on the astrolabe. Since then, goniometers have become important tools in many areas of science and technology, helping people measure and work with angles very accurately.

Protractor

A protractor is a measuring instrument used for measuring angles. It is usually made of clear plastic and comes in different shapes, like half-discs or full circles. Some protractors have arms that move to help measure angles more accurately.

A half-circle protractor marked in degrees (180°).

Most protractors measure angles in degrees (°), but some use radians. Many are split into 180 equal parts, and some even smaller parts called arcminutes. A protractor that uses centiturns is often called a "percentage protractor".

A special kind of protractor is the bevel protractor. It has a pivoted arm and can measure angles very precisely. It is often used in drawing and making tools. This type of protractor can read angles as small as 5 arcminutes and measure angles from 0° to 450°. It has a beam, a dial with numbers, and a blade connected to a plate. To measure angles, you look at where a mark on the plate lines up with numbers on the dial.

Applications

Surveying

Before the invention of the theodolite, the goniometer was used in surveying. It helped measure angles in land surveys using simple tools like protractors with weights.

In military topography

Military tools often combine protractors, rulers, and scales to measure directions and distances on maps. These tools are made from flexible plastic to avoid distortions.

Royal Artillery Mils Protractor

Since the 1960s, special protractors have been made for use in conflicts like the Vietnam War. These tools help soldiers measure angles and directions on maps.

Manual (1), and Mitscherlich's optical (2) goniometers for use in crystallography, c. 1900

GTA 05-02-012 Coordinate Scale and Protractor

Since 1981, this standardized tool has been used by the U.S. Army to help soldiers find their way and measure angles on maps. It is included in backpacks of many military personnel.

Combat Mission Plotter

Special plotters combine protractors, rulers, and scales to help plan combat missions by drawing symbols on maps.

GPS Plotting Protractor

This protractor helps measure positions accurately using GPS. It is useful when navigation tools are not working well.

Communications

Goniometers were used in early radio direction finding systems to determine the direction of radio signals. These tools are still used today in both military and civilian settings.

Crystallography

In the study of crystals, goniometers measure angles between crystal faces and are used to rotate samples in X-ray diffraction experiments.

Light measurement

Goniophotometers measure how light spreads out in different directions.

In medicine

Goniometers are used by healthcare workers to measure how much a joint can move. This helps track recovery after injuries.

Rehabilitative therapy

In therapy, goniometers measure how much a joint can move to track progress in rehabilitation programs.

Surface science

Contact angle goniometer

In surface science, a contact angle goniometer measures the angles where liquids meet surfaces. It was first designed in Washington, D.C. and has been improved with cameras and software.