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Goniometer made by Develey le Jeune in Lausanne, late 18th–early 19th century
Manual (1), and Mitscherlich's optical (2) goniometers for use in crystallography, c. 1900

A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry is derived from two Greek words, gōnia, meaning angle, and metron, meaning measure.

The first description of a goniometer, derived from the astrolabe, was apparently in 1538, by Gemma Frisius.




Prior to the invention of the theodolite, the goniometer was used in surveying. The application of triangulation to geodesy was described in the second (1533) edition of Cosmograficus liber by Petri Appiani as a 16-page appendix by Frisius entitled Libellus de locorum describendorum ratione.[1]


The Bellini–Tosi direction finder was a type of radio direction finder that was widely used from World War I to World War II. It used the signals from two crossed antennas, or four individual antennas simulating two crossed ones, to re-create the radio signal in a small area between two loops of wire. The operator could then measure the angle to the target radio source by performing direction finding within this small area. The advantage to the Bellini–Tosi system is that the antennas do not move, allowing them to be built at any required size.

The basic technique remains in use, although the equipment has changed dramatically. Goniometers are widely used for military and civil purposes,[2] e.g. interception of satellite and naval communications on the French warship Dupuy de Lôme uses multiple goniometers.


In crystallography, goniometers are used for measuring angles between crystal faces. They are also used in X-ray diffraction to rotate the samples. The groundbreaking investigations of physicist Max von Laue and colleagues into the atomic structure of crystals in 1912 involved a goniometer.

Light measurementEdit

Goniophotometers measure the spatial distribution of light visible to the human eye at a specific angular position.

In medicineEdit

A goniometer is used to document initial and subsequent range of motion, at the visits for occupational injuries, and by disability evaluators to determine a permanent disability. This is to evaluate progress, and also for medico-legal purposes. It is a tool to evaluate Waddell's signs (findings that may indicate symptom magnification.)

Rehabilitative therapyEdit

In physical therapy, occupational therapy and athletic training, a goniometer is an instrument which measures range of motion joint angles of the body. This measurement instrument is a helpful, clinical tool that allows for objective measurements in order to accurately track progress in a rehabilitation program. When a patient has a decreased range of motion, a therapist will assess the joint before performing an intervention and will continue to use the tool to make sure that progress is made. These range of motion measurements can be taken at any joint and they typically involve some knowledge about the anatomy of the body, particularly bony landmarks. For example, when measuring the knee joint, the axis (point of rotation) would be placed on the lateral epicondyle of the femur, while the stationary arm would be lined up with the greater trochanter of the femur. Finally, the moveable arm of the goniometer would be lined up with the lateral malleolus of the fibula and a measurement will be taken using the degree scale on the circular portion of the tool. The only problem with goniometers is the accuracy of the reading is not always the greatest. Issues with the intra-measure (between measures) and inter-tester (between clinicians) reliability seem to increase as the experience of the examiner decreases. Some studies suggest that these errors can be anywhere between 5 and 10 degrees when completing repeated measures[citation needed].

These goniometers do come in different forms that some would argue will actually increase the reliability of the tool.[3][4] The universal standard goniometer is a plastic or metal tool with 1 degree increments. The arms usually are not longer than 12-inches so it can be hard to accurately pinpoint the exact landmark needed for measurement. A more reliable goniometer would be the telescopic-armed goniometer. There is a plastic circular axis as a classic goniometer but the arms extend out to as long as two feet in either direction.

More recently in the twenty-first century, smartphone application developers have created mobile applications that are intended to perform like a goniometer. These applications (such as Knee Goniometer and Goniometer Pro) use the accelerometers in phones to calculate the angles of the joints measured. There has been a lot of research recently that supports these applications and their devices as reliable and valid tools that have just as much accuracy as a universal goniometer.[5][6][7]

Modern rehabilitative therapy motion capture systems perform goniometry at the very least measuring active range of motion[8]. While in some cases accuracy may be inferior to using a goniometer, measuring angles using a motion capture system is superior in providing measurement during dynamic, as opposed to static situations. Furthermore, use of a traditional goniometer takes valuable time. In the clinical context, performing manual measurements takes valuable time and may not be practical.

Surface scienceEdit

Contact angle goniometerEdit

Surface scientists use a contact angle goniometer to measure contact angle, surface energy and surface tension.
In a contact angle measurement, the angle between the droplet and solid surface indicates the wettability of the surface.

In surface science, an instrument generally called a contact angle goniometer or tensiometer is used to measure the static contact angle, advancing & receding contact angles, and in some cases surface tension. The first contact angle goniometer was designed by Dr. William Zisman of the United States Naval Research Laboratory in Washington, D.C. and manufactured by ramé-hart (now ramé-hart instrument company), New Jersey, USA. The original manual contact angle goniometer used an eyepiece with microscope. Today's contact angle goniometer uses a camera and software to capture and analyze the drop shape and is better suited for dynamic and advanced studies.

Surface tensionEdit

Surface tension exists because the molecules inside a liquid experience roughly equal cohesive forces in all directions, but molecules at the surface experience larger attractive forces toward the liquid than toward gas

Contact angle goniometers (q.v.)can also determine the surface tension for any liquid in gas or the interfacial tension between any two liquids. If the difference in densities between the two fluids is known, the surface tension or interfacial tension can be calculated by using the pendant drop method. An advanced instrument often called a goniometer / tensiometer will include software tools to measure surface tension and interfacial tension using the pendant drop, inverted pendant drop, and sessile drop methods - in addition to contact angle.

A centrifugal adhesion balance is used to relate the contact angles to the adhesion of the drop to the surface.

A gonioreflectometer is used to measure the reflectivity of a surface at a variety of angles.


A miniature electro-mechanical goniometer stage. This type of stage is used primarily in the field of lasers and optics.

A positioning goniometer or goniometric stage is a device used to rotate an object precisely about a fixed axis in space. It is similar to a linear stage, however, rather than moving linearly with respect to its base, the stage platform rotates partially about a fixed axis above the mounting surface of the platform. Positioning goniometers typically use a worm drive with a partial worm wheel fixed to the underside of the stage platform meshing with a worm in the base. The worm may be rotated manually or by a motor as in automated positioning systems.

Knife and blade cutting edge angle measurementEdit

The included cutting angles of all kinds of sharp edge blades is measured using a laser reflecting goniometer. Developed by the Cutlery and Allied Trades Research Association (CATRA) in the UK, a range of devices can accurately determine the cutting edge profile including a rounding of the tip to ½°. The included angle of a blade is important in controlling its cutting ability and edge strength, i.e. a low angle makes the edge thin and optimized for cutting while a large angle makes it thick, which cuts poorly, but is very strong.

Doctor blade inspectionEdit

Used doctor blades, from gravure and other printing and coating processes, may be inspected using a goniometer, typically with a built-in light source, to examine the blade edge to see whether the blade has worn at the desired angle and whether there are signs of wear at other angles. A difference in angle from that set on the machine may indicate excessive pressure, and a range of angles ("rounding") probably indicates a lack of stiffness, or wear, in the blade holder assembly.

See alsoEdit


  1. ^ Claude Brezinski and Dominique Tournès, André-Louis Cholesky: Mathematician, Topographer, and Army Officer, Birkhäuser, Basel (2014) ISBN 978-3-319-08134-2
  2. ^ Jacqueline Boucher (2007-05-03). "Radio receiver workload accelerates". Retrieved 2007-09-21. 
  3. ^ Milanese, Gordon. "Reliability and concurrent validity of knee angle measurement: Smart phone app versus universal goniometer used by experienced and novice clinicians". Manual Therapy. 5: 1–6. 
  4. ^ Jones, Sealey. "Concurrent validity and reliability of the simple goniometer iPhone app compared with the universal goniometer". Physiotherapy Theory and Practice. 30 (7): 512–516. 
  5. ^ Ockendon, Matthew. "Validation of a novel smartphone accelerometer-based knee goniometer". The Journal of Knee Surgery. 25 (4): 341–345. 
  6. ^ Jones, A (2014). "Concurrent validity and reliability of the simple goniometer iphone app compared with the universal goniometer". Physiotherapy Theory and Practice. 30 (7): 512–516. 
  7. ^ Kuegler, P.; Wurzer, P.; Tuca, A.; et al. (2015). "Goniometer-apps in hand surgery and their applicability in daily clinical practice". Safety in Health. 1: 11. doi:10.1186/s40886-015-0003-4. 
  8. ^ "Markerless Motion Capture. Biomechanical Analysis | EuMotus". Retrieved 2018-01-15. 

External linksEdit