Likert scale calculator
Turn the counts for one survey question into a mean, median, percent agree and margins of error.
One count for each answer option, from the lowest (for example “strongly disagree”) to the highest, separated by commas or spaces. Include zeros. From 3 to 11 options.
What does this calculator summarize?
It takes the number of respondents who chose each answer on a single Likert-type item (for example 1 = strongly disagree to 5 = strongly agree) and returns the numbers people usually report: the mean, standard deviation, median and mode, the top-2-box and bottom-2-box shares, and confidence intervals. Enter the counts from the lowest option to the highest, separated by commas, one count per option and including zeros. A Likert scale in the strict sense is the sum or average of several such items; a single item with agree–disagree labels is a Likert-type item, and the summary below is what you would report for it.
Worked example: 100 responses on a 5-point agreement item
Counts of 5, 10, 20, 40, 25 for options 1 to 5 give n = 100 and a mean of (5×1 + 10×2 + 20×3 + 40×4 + 25×5) ÷ 100 = 3.70. The sample standard deviation is 1.11, the median is 4 (the cumulative share first passes 50% at option 4) and the mode is 4. Top-2-box, the share choosing 4 or 5, is 65.0%, and bottom-2-box, the share choosing 1 or 2, is 15.0%. A 95% Wilson interval for the top-2-box share is 55.3% to 73.6%; the simpler “p ± 1.96 × √(p(1 − p) ÷ n)” formula gives ±9.3 points. The interval for the mean, from the t distribution, is 3.48 to 3.92.
Is it legitimate to calculate a mean of Likert responses?
It is one of the long-running arguments in survey research. The strict view says Likert responses are ordinal: the step from “agree” to “strongly agree” need not equal the step from “neutral” to “agree”, so only the median, mode and percentages are meaningful. Geoff Norman’s 2010 paper in Advances in Health Sciences Education (15:625–632), “Likert scales, levels of measurement and the ‘laws’ of statistics”, argues the opposite for analysis: parametric methods such as ANOVA, regression and correlation can be used with ordinal Likert data and are generally robust. We have only read summaries of the full text, so treat that as the paper’s thesis, not a verdict. A practical compromise is to report the mean and SD together with the full distribution and the top-box share, so a reader who distrusts the mean still has the percentages.
What are top-2-box and bottom-2-box?
Top-2-box is the share of respondents who chose the two most favorable options (4 or 5 on a 5-point scale), often reported as “percent agree”. Bottom-2-box is the share choosing the two least favorable. They make a skewed distribution easier to talk about than a mean does: in the example, 65.0% agree even though the mean is only 3.70. On scales with other lengths, “2-box” is still the two end options at the favorable end; on a 7-point scale some teams report top-3-box instead, so state which one you used. The calculator uses the top two and bottom two options of the number you entered.
How do I read the margin of error?
The percent-agree figure is a proportion, so it carries sampling error like any poll: the interval shows the range of true shares compatible with your sample. The Wilson interval behaves better than the textbook formula for small samples and for shares near 0% or 100%, which is why both are shown. The intervals assume a random sample; a self-selected sample (a website pop-up, an email to people who already like you) has bias that no margin of error can measure. A low response rate, the topic of our survey response rate calculator, makes this worse.
How is the median calculated when responses split evenly?
The median is the option where the cumulative share first passes 50%. If exactly half of the responses lie at or below one option and the other half above, the median falls between the two, and the calculator reports their average, for example counts of 0, 5, 5, 0, 0 give a median of 2.5. With a 5-point scale the median can only take a few values, which is one reason it is a blunt tool for comparing groups. Several modes can occur when options tie, and the calculator lists all of them.
Common mistakes
Do not average items that are worded in opposite directions without first reverse-coding them: a “strongly agree” to “I hate this product” is a negative result. Do not compare means from scales of different length without rescaling, since 4.0 on a 5-point item and 4.0 on a 7-point item are different things. And do not rank groups by tiny differences in means when the intervals overlap: the standard error of the mean is the SD divided by √n, so a few hundred responses are needed to tell apart groups that differ by a tenth of a point. For reliability across several items of the same scale, use the Cronbach’s alpha calculator.
For general information only. Sources: G. Norman, “Likert scales, levels of measurement and the ‘laws’ of statistics,” Advances in Health Sciences Education 15(5) (2010) 625–632, doi:10.1007/s10459-010-9222-y (citation confirmed from the author’s university record; the full text was not opened, so its argument is summarized from secondary descriptions); E. B. Wilson (1927) interval for a proportion and the t-based interval for a mean are standard methods. Related: margin of error calculator, Net Promoter Score calculator and survey response rate calculator. How we check our calculators.