Krejcie and Morgan Sample Size Table
Look up the sample size for a given population in the Krejcie and Morgan (1970) table, or enter any population size to apply the same formula. The table assumes 95% confidence, a ±5% margin of error and P = 0.50. Calculations run in your browser; nothing you enter is sent or stored.
Krejcie and Morgan sample size
completed responses
For a population of 1,000 (27.8% of it), at 95% confidence, ±5% margin of error and P = 50%.
- Formula before rounding
- 277.71
- Rounded up (conservative)
- 278
- Published table row
- N = 1,000 → S = 278
Need to plan invitations from a response rate, or use a large or unknown population? Use the sample size calculator for surveys.
How this number was calculated
- 1X² = 3.841, chi-square with 1 degree of freedom at 95% confidence
- 2s = 3.841 × 1,000 × 0.5 × 0.5 ÷ [0.05² × (1,000 − 1) + 3.841 × 0.5 × 0.5] = 277.71
- 3Round to the nearest whole number, as the published table does: 278
Methods statement
The sample size was determined with the Krejcie and Morgan (1970) table and formula, s = X²NP(1 − P) / [d²(N − 1) + X²P(1 − P)], for a population of N = 1,000, with X² = 3.841 (95% confidence), P = 0.5 and a margin of error of d = 0.05. This gives s = 277.71, so a minimum of 278 completed responses was required.
Krejcie and Morgan table (1970)
Table for determining sample size from a given population. N is the population size and S the sample size, at 95% confidence (X² = 3.841), P = 0.50 and d = 0.05. The highlighted row is the one for your population.
| Population N | Sample S |
|---|---|
| 10 | 10 |
| 15 | 14 |
| 20 | 19 |
| 25 | 24 |
| 30 | 28 |
| 35 | 32 |
| 40 | 36 |
| 45 | 40 |
| 50 | 44 |
| 55 | 48 |
| 60 | 52 |
| 65 | 56 |
| 70 | 59 |
| 75 | 63 |
| 80 | 66 |
| 85 | 70 |
| 90 | 73 |
| 95 | 76 |
| 100 | 80 |
| 110 | 86 |
| 120 | 92 |
| 130 | 97 |
| 140 | 103 |
| 150 | 108 |
| 160 | 113 |
| 170 | 118 |
| 180 | 123 |
| 190 | 127 |
| 200 | 132 |
| 210 | 136 |
| Population N | Sample S |
|---|---|
| 220 | 140 |
| 230 | 144 |
| 240 | 148 |
| 250 | 152 |
| 260 | 155 |
| 270 | 159 |
| 280 | 162 |
| 290 | 165 |
| 300 | 169 |
| 320 | 175 |
| 340 | 181 |
| 360 | 186 |
| 380 | 191 |
| 400 | 196 |
| 420 | 201 |
| 440 | 205 |
| 460 | 210 |
| 480 | 214 |
| 500 | 217 |
| 550 | 226 |
| 600 | 234 |
| 650 | 242 |
| 700 | 248 |
| 750 | 254 |
| 800 | 260 |
| 850 | 265 |
| 900 | 269 |
| 950 | 274 |
| 1,000 | 278 |
| 1,100 | 285 |
| Population N | Sample S |
|---|---|
| 1,200 | 291 |
| 1,300 | 297 |
| 1,400 | 302 |
| 1,500 | 306 |
| 1,600 | 310 |
| 1,700 | 313 |
| 1,800 | 317 |
| 1,900 | 320 |
| 2,000 | 322 |
| 2,200 | 327 |
| 2,400 | 331 |
| 2,600 | 335 |
| 2,800 | 338 |
| 3,000 | 341 |
| 3,500 | 346 |
| 4,000 | 351 |
| 4,500 | 354 |
| 5,000 | 357 |
| 6,000 | 361 |
| 7,000 | 364 |
| 8,000 | 367 |
| 9,000 | 368 |
| 10,000 | 370 |
| 15,000 | 375 |
| 20,000 | 377 |
| 30,000 | 379 |
| 40,000 | 380 |
| 50,000 | 381 |
| 75,000 | 382 |
| 1,000,000 | 384 |
Every value is recalculated from the formula and matches the table printed in Krejcie and Morgan (1970), Educational and Psychological Measurement, 30(3), 607–610.
The Krejcie and Morgan formula
Krejcie and Morgan built their table from a single formula for the sample size needed to estimate a population proportion:
s = X²NP(1 − P) / [d²(N − 1) + X²P(1 − P)]
- s
- The required sample size: the number of completed, usable responses.
- N
- The population size.
- X²
- The chi-square value for 1 degree of freedom at the chosen confidence level: 3.841 for 95%, as in the table (2.706 for 90% and 6.635 for 99%).
- P
- The population proportion. The table assumes 0.50, which gives the largest sample size.
- d
- The degree of accuracy, or margin of error, as a proportion: 0.05 means ±5 percentage points.
For N = 1,000: s = 3.841 × 1,000 × 0.5 × 0.5 / [0.05² × 999 + 3.841 × 0.5 × 0.5] = 960.25 / 3.458 = 277.71, which the table lists as 278. The table rounds s to the nearest whole number.
How to read the table
- Find your population size in the N column.
- Read the sample size next to it in the S column. That is the number of completed responses you need.
- If your exact N is not listed, use the next larger N, which gives a slightly larger sample, or type your N into the calculator above.
For a population of 350, the next listed row is N = 360 with S = 186. The formula for N = 350 gives 183.38, so 183 by the table’s rounding or 184 if you round up.
The sample size rises quickly for small populations and then levels off: 80 for 100 people, 278 for 1,000, 370 for 10,000 and 384 for 1,000,000. Beyond a few thousand, the population size hardly matters.
Krejcie and Morgan, Cochran and Yamane
The Krejcie and Morgan formula is Cochran’s formula for a proportion with the finite population correction, written with X² in place of z² (they are equal for 1 degree of freedom). Yamane’s n = N / (1 + Ne²) is a simplification that fixes 95% confidence and P = 0.50.
| Population N | Krejcie and Morgan | Cochran, rounded up | Yamane |
|---|---|---|---|
| 100 | 80 | 80 | 80 |
| 500 | 217 | 218 | 223 |
| 1,000 | 278 | 278 | 286 |
| 5,000 | 357 | 357 | 371 |
| 10,000 | 370 | 370 | 385 |
| 1,000,000 | 384 | 384 | 400 |
Krejcie and Morgan and Cochran differ by at most one response here, from rounding to the nearest number rather than up. Yamane is slightly more conservative. If a reviewer asks for one specific method, state which you used; the sample size calculator shows Cochran’s steps for any confidence level and margin.
Assumptions and when not to use the table
- Simple random sampling. Every member of the population must have an equal chance of selection, drawn without replacement from a complete list. Convenience, snowball and volunteer samples cannot be justified by sample size alone.
- One proportion. The table sets the precision of an estimated percentage. It is not a power analysis for comparing groups, testing hypotheses or clinical trials, and it does not cover means, correlations or regression.
- Fixed settings. The printed values hold only for 95% confidence, ±5 points and P = 0.50. Use the calculator’s settings for other values.
- Completed responses. S counts usable responses, not invitations. Divide by the expected response rate to plan invitations, and remember that inviting more people does not remove nonresponse bias.
- Subgroups. If you need ±5% for each department, school or region, each subgroup needs its own sample size.
How to cite Krejcie and Morgan (1970)
APA 7th edition reference:
Krejcie, R. V., & Morgan, D. W. (1970). Determining sample size for research activities. Educational and Psychological Measurement, 30(3), 607–610. https://doi.org/10.1177/001316447003000308
In-text: (Krejcie & Morgan, 1970). An example methods sentence: “For a population of 1,000, a sample of 278 completed responses was required according to Krejcie and Morgan (1970), at 95% confidence and a ±5% margin of error.” The calculator above writes this sentence for your own numbers.
For other styles, paste the DOI into the citation generator for Vancouver, AMA, Harvard, MLA, Chicago or BibTeX.
Frequently asked questions
- What is the Krejcie and Morgan table?
- It is a table published by Robert V. Krejcie and Daryle W. Morgan in 1970 in Educational and Psychological Measurement. It lists the sample size S needed for a population of size N, from N = 10 to N = 1,000,000, so that a proportion can be estimated to within ±5 percentage points with 95% confidence, assuming P = 0.50.
- What is the Krejcie and Morgan formula?
- s = X²NP(1 − P) / [d²(N − 1) + X²P(1 − P)], where s is the sample size, N the population size, X² the chi-square value for 1 degree of freedom at the chosen confidence level (3.841 for 95%), P the population proportion (0.50 for the largest sample) and d the margin of error as a decimal (0.05).
- What sample size does the Krejcie and Morgan table give for a population of 1,000?
- For N = 1,000 the table gives S = 278. Other common rows are 80 for 100, 217 for 500, 322 for 2,000, 357 for 5,000, 370 for 10,000 and 384 for 1,000,000.
- What if my population size is not in the table?
- Either use the next larger population listed, which gives a slightly larger and therefore conservative sample, or enter your exact population in the calculator, which applies the same formula. For N = 350, the next row is 360 with S = 186, while the formula gives 183.38, which the table convention rounds to 183.
- Why does the table never go above 384?
- As the population grows, the formula approaches X²P(1 − P) / d² = 3.841 × 0.25 / 0.0025 = 384.1, so the sample size levels off. For N = 1,000,000 the table gives 384. Calculators that use z = 1.96 and always round up give 385 for a large or unknown population; the difference is only rounding.
- Is Krejcie and Morgan the same as Cochran’s formula?
- Yes, in substance. The Krejcie and Morgan formula is algebraically identical to Cochran’s formula for a proportion with the finite population correction, because X² with 1 degree of freedom equals z². Small differences come from using 3.841 instead of 1.959964² and from rounding to the nearest whole number instead of rounding up.
- What is the difference between Krejcie and Morgan and Yamane?
- Yamane’s formula, n = N / (1 + Ne²), is a simplified version that fixes 95% confidence and P = 0.50 and gives slightly larger samples, for example 286 instead of 278 for N = 1,000 and 400 instead of 384 for very large populations. Krejcie and Morgan lets you state the confidence level and proportion explicitly.
- Can I use the Krejcie and Morgan table when the population is unknown?
- If the population is very large or unknown, the last row applies: about 384 completed responses at 95% confidence and ±5%. To change the margin of error or confidence level, or to plan invitations with a response rate, use the sample size calculator for surveys and proportions.
- Does the table give the number of people to invite?
- No. S is the number of completed, usable responses. Divide it by your expected response rate to estimate how many people to invite: 278 completed responses at a 40% response rate needs about 695 invitations. A larger invitation list does not remove nonresponse bias.
- When should I not use the Krejcie and Morgan table?
- Do not use it for comparing groups, testing a hypothesis or clinical trials, which need a power analysis; for estimating means, correlations or regression models; for subgroups that each need their own precision; or for convenience and snowball samples, because the table assumes simple random sampling. It also does not apply to qualitative studies.
- How do I cite the Krejcie and Morgan table in APA style?
- Krejcie, R. V., & Morgan, D. W. (1970). Determining sample size for research activities. Educational and Psychological Measurement, 30(3), 607–610. https://doi.org/10.1177/001316447003000308. In the text, cite it as (Krejcie & Morgan, 1970).
- Is there a Krejcie and Morgan table PDF?
- The original article is available from the publisher through its DOI. On this page you can download the full table as a CSV file or open a print view and save it as a PDF; both include the citation and the assumptions behind the numbers.
Sources
- Krejcie RV, Morgan DW. Determining sample size for research activities. Educ Psychol Meas. 1970;30(3):607–610. Source of the table and formula.
- Cochran WG. Sampling Techniques. 3rd ed. New York: John Wiley & Sons; 1977. The proportion formula and finite population correction.
- Yamane T. Statistics: An Introductory Analysis. 2nd ed. New York: Harper and Row; 1967.
- Israel GD. Determining Sample Size (PEOD6). University of Florida IFAS Extension.
Content updated October 26, 2026. The table on this page is recalculated from the published formula and checked against every printed value.