Letters To The Editor Open Access
Copyright ©The Author(s) 2016. Published by Baishideng Publishing Group Inc. All rights reserved.
World J Virol. May 12, 2016; 5(2): 85-86
Published online May 12, 2016. doi: 10.5501/wjv.v5.i2.85
Determination of 50% endpoint titer using a simple formula
Muthannan Andavar Ramakrishnan
Muthannan Andavar Ramakrishnan, Division of Virology, Indian Veterinary Research Institute, Uttarakhand 263138, India
Author contributions: Ramakrishnan MA designed, validated the assay and wrote the letter.
Conflict-of-interest statement: None.
Open-Access: This article is an open-access article which was selected by an in-house editor and fully peer-reviewed by external reviewers. It is distributed in accordance with the Creative Commons Attribution Non Commercial (CC BY-NC 4.0) license, which permits others to distribute, remix, adapt, build upon this work non-commercially, and license their derivative works on different terms, provided the original work is properly cited and the use is non-commercial. See: http://creativecommons.org/licenses/by-nc/4.0/
Correspondence to: Muthannan Andavar Ramakrishnan, Senior Scientist, Division of Virology, Indian Veterinary Research Institute, Mukteswar Campus, Uttarakhand 263138, India. maramakrishnan@gmail.com
Telephone: +91-5942-286346 Fax: +91-5942-286347
Received: January 7, 2016
Peer-review started: January 10, 2016
First decision: March 1, 2016
Revised: March 2, 2016
Accepted: March 17, 2016
Article in press: March 19, 2016
Published online: May 12, 2016


Two commonly used methods for calculating 50% endpoint using serial dilutions are Spearman-Karber method and Reed and Muench method. To understand/apply the above formulas, moderate statistical/mathematical skills are necessary. In this paper, a simple formula/method for calculating 50% endpoints has been proposed. The formula yields essentially similar results as those of the Spearman-Karber method. The formula has been rigorously evaluated with several samples.

Key Words: Endpoint dilution, TCID50, Spearman-Karber, Reed and Muench

Core tip: The formula described in this manuscript can be used to calculate 50% endpoint titre such as TCID50%, LD50, TD50, etc., in addition to the currently existing methods. The proposed formula can be applied without the help of calculator or computer.


Currently, there are two methods (formulas) viz., Reed and Muench[1] and Spearman-Karber[2,3] are commonly employed for the calculation of 50% endpoint by serial dilution. To understand/apply these methods, moderate mathematical skills along with calculator or computer are essential. Here, I have proposed a simple formula to calculate the 50% endpoint titre and this formula can be used in addition to Reed and Muench or Spearman-Karber, methods but not exclusively at this point. In the following section, the newly proposed method is compared with two commonly used methods viz., Reed and Muench and Spearman-Karber.

Reed and Muench method

log10 50% end point dilution = log10 of dilution showing a mortality next above 50% - (difference of logarithms × logarithm of dilution factor).

Generally, the following formula is used to calculate “difference of logarithms” (difference of logarithms is also known as “proportionate distance” or “interpolated value”): Difference of logarithms = [(mortality at dilution next above 50%)-50%]/[(mortality next above 50%)-(mortality next below 50%)].

Spearman-Karber method

log10 50% end point dilution = - (x0 - d/2 + d ∑ ri/ni)

x0 = log10 of the reciprocal of the highest dilution (lowest concentration) at which all animals are positive;

d = log10 of the dilution factor;

ni = number of animals used in each individual dilution (after discounting accidental deaths);

ri = number of positive animals (out of ni).

Summation is started at dilution x0.

Newly proposed method

Formula 1:

log10 50% end point dilution = -[(total number of animals died/number of animals inoculated per dilution) + 0.5] × log dilution factor.

Formula 2 (if any accidental death occurred):

log10 50% end point dilution = -(total death score + 0.5) × log dilution factor.

Comparison of the newly proposed and existing methods with an example of virus titration in mice: For simplicity, it is assumed that 1 mL of each dilution was inoculated (Table 1, Table 2 and Table 3).

Table 1 Calculation of virus titre in mice using the Reed and Muench method.
Log10 virus dilutionMice
Cumulative total
Percent mortality
-11005705757/57 × 100 = 100
-21004704747/47 × 100 = 100
-31003703737/37 × 100 = 100
-41002702727/27 × 100 = 100
-51001701717/17 × 100 = 100
-66474117/11 × 100 = 63
-719113141/14 × 100 = 7
Table 2 Calculation of virus titre in mice using the Spearman-Karber method.
Log10 virus dilutionMice
Table 3 Calculation of virus titre in mice using the new method.
Log10 virus dilutionMice
Death score
-1101010/10 = 1
-2101010/10 = 1
-3101010/10 = 1
-4101010/10 = 1
-5101010/10 = 1
-66106/10 = 0.6
-71101/10 = 0.1

The newly proposed formula has been intensively validated with several samples and essentially yields the same results as those by the Spearman-Karber method. Therefore, the newly proposed method can be used in addition to the existing methods but not exclusively at this point.


P- Reviewer: Bharaj P, Ghiringhelli PD S- Editor: Ji FF L- Editor: A E- Editor: Lu YJ

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