Angle measurement

Accurate angle measurements are fundamental to applications in industry, research, safety and trade. METAS supports industry, laboratories and public authorities by providing calibration services for angle standards and angle measuring instruments.

Angle measurement in everyday life

Angle measurement is a distinctive aspect of dimensional metrology. Unlike length and other dimensional quantities, the angle is not directly defined in terms of an SI base unit, but through the division of a complete circle. Angle measurements are typically used in quality assurance and manufacturing metrology to verify the geometric alignment of workpieces, surfaces and axes. They are particularly common in machine tools, coordinate measuring machines and optical measurement systems. In calibration, angle measurements are also used to verify and establish the metrological traceability of angle measuring instruments.

Typical applications of angle measurements

Angle measurements are used to determine squareness, parallelism, inclination and specified angle values in a wide range of applications:

• Machine tools: angular errors of machine axes, for example in turn-milling machines
• Diffraction angles
• Coordinate measuring machines: squareness and alignment of the X, Y and Z axes
• Optics: angles of lenses and mirrors
• Robotics: joint and axis angles of industrial robots
• Mechanical engineering: angular position and alignment of guides, slides and assemblies

Our services in the field of angle measurement

Calibrations

We offer calibration services for, among others, the following angle standards and angle measuring instruments:

• Autocollimators and electronic inclinometers
• Optical polygons
• Rotary encoders, rotary tables and indexing rotary tables
• Angular gauge blocks
• Granite square

A detailed overview of our calibration services in the field of angle measurement can be found in our service catalogue and in our CMC entries in the KCDB.

• Services catalogue: Laboratory for Length, Nano- and Microtechnology

  PDF415.15 kB1 June 2025

• Key Comparison Database (KCDB)

Is the service you are looking for not listed on the website? Please do not hesitate to contact us so that we can work together to find a customised solution to your problem.

Measuring methods and technologies

Angle division

The national standard for angle measurements at METAS consists of an air-bearing rotary table. The measuring system has a resolution of 0.035". Driven by a friction wheel and a piezo actuator for fine positioning, the table can be numerically controlled.

By the use of self-calibrating methods in combination with an indexing table and an optical polygon the table is numerically corrected, achieving thus an accuracy of better than 0.1".

The angle measuring table described is the basis for the calibration of angle standards, such as angle block gauges, optical polygons, indexing tables and incremental encoders.

Small angles

Small angles are preferably generated with sine bars, i.e. by the ratio of two lengths. These are used to calibrate electronic levels or autocollimators. An angle interferometer, which can be mounted on the numerically controlled rotary table, provides a resolution of 0.008" and thus allows for the calibration of autocollimators in a large range. A 200 mm long mirror bar made from Zerodur, supported on a flexure pivot and driven by a piezo-electric actuator can generate rotational angles in a range of ±7" and 0.001" resolution for highest accuracy applications.

Quality and expertise

You can find information on the quality of our services on the “Integrated Management System” page.

Enquiry and contact

Laboratory Length, Nano- and Micro-Technology
Federal Institute of Metrology METAS
Lindenweg 50
3003 Bern-Wabern

T [phone]
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