# Font size calculator

Minimum size

(Enlarged depiction of visual angle)

## General notes

The Font Size Calculator is designed to make it easier to identify inclusive font sizes in compliance with the German DIN 1450 standard on legibility. Depending on the relevance of compliance with specific standards, further examination based on all the criteria of DIN 1450 and possibly on other standards may be necessary.

A summary of information on this topic can be found in the chapter on font sizes (in German) and more detailed information is available in DIN 1450 (in German).

The recommendations on font sizes in DIN 1450 are based on normally sharp vision of at least 70 % (visual acuity ≥ 0.7). Font sizes can be multiplied by a factor appropriate for the visual acuity of people whose vision is less sharp to provide them with an adequate font size. Font size cannot however be enlarged arbitrarily because of the limits set by the reader’s field of vision, column widths, formats and technical reading aids. Factors ranging from 1.4 (visual acuity ≥ 0.5) up to a maximum of 1.75 (visual acuity ≥ 0.4) have been shown to be practicable. Using these factors, font size can be multiplied for texts that are specially designed for readers with visual impairments. The standard font sizes recommended in DIN 1450 are sufficient for all other applications.

## The background to the calculation

The calculation of font size as prescribed in DIN 1450 is based on x-heights. Font size (here x-height) is generally set depending on the viewer’s distance from it. The shorter a viewer’s distance from a text is, the smaller its font can be and vice-versa. DIN 1450 bases its recommendations for x-heights that function independent of the viewer’s distance on the visual angle.

The visual angle is the angle at which a viewed object is perceived. Minimum x-height values for the three types of text in DIN 1450, reading text, consultation text and signalling text, are expressed through the visual angle in the unit of arc minutes. For more information see also the Wikipedia articles on angular diameter and visual acuity.

Based on the minimum values stipulated in DIN 1450 for the prescribed visual angle α, the x-height M can be determined, taking the viewer’s distance D into account, through a calculation using an isosceles triangle.

$M=2D×\mathrm{tan}\left(\frac{\alpha }{2}\right)$

DIN 1450 also makes it possible to take the viewer’s sharpness of vision (visual acuity) and adaptive luminance (or more simply ‘lighting’) of the signifier into account in the calculation by including these two aspects as the Luminance/Visual Acuity-Correction factor KLV in the calculation as follows:

$M=2D×\mathrm{tan}\left(\frac{\alpha ×{K}_{LV}}{2}\right)$

The Luminance/Visual acuity Correction factor KLV can be derived from Table A.1 in DIN 1450 as follows:

${K}_{LV}=\frac{L{f}_{V1}}{V}$

LfV1 corresponds with the Luminance Correction factor shown in column 1 for a visual acuity of 1. V represents the viewer’s visual acuity.

In almost every computer programme you can adjust font size (actually body height) but not x-height. To calculate font size from the calculated x-height, the x-height-font size ratio MS of the font to be used must be known. This can vary from font to font and vary greatly in some cases. It can be identified by measuring the x-height of a known font size to determine the ratio between the x-height M and font size S:

${M}_{S}=\frac{M}{S}$

If no individually determined value is entered in the prescribed field, the Font Size Calculator assumes an x-height-font size ratio of 0.47 as standard. This can be obtained from DIN 1450. The specification of recommended font size in points is in this case only a rough value. In contrast, the calculation of x-height in millimetres is always exact.

### Special features of calculating font sizes for screens

Some special features apply to calculating font sizes for screen display (see also Digital Media). Here the device’s virtual resolution must be specified in pixels per inch (ppi) in an extra field.