Sample Size Calculator — Free Online Survey Size Tool

How to Use the Sample Size Calculator

1. Select the confidence level: Choose how confident you want to be that your results capture the true population value. 95% is the most widely used standard. Higher confidence requires larger samples.
2. Enter the margin of error: Specify the maximum acceptable margin of error as a percentage. For example, entering 5 means you want results accurate to ±5%. Smaller margins of error require larger samples. The typical range for survey research is 3% to 10%.
3. Enter the expected proportion: If you have prior knowledge about the population proportion, enter it here (as a percentage). If unknown, leave it at 50% for the most conservative (largest) sample size estimate. This parameter has the biggest impact when it deviates significantly from 50%.
4. Enter the population size (optional): If your population is finite and known, enter the total size. This applies the finite population correction, which reduces the required sample size. Leave at 0 if the population is very large or unknown.
5. Read the results: The required sample size is displayed prominently. If you entered a population size, the adjusted sample size with finite population correction is also shown, along with the unadjusted value for comparison.

Remember to account for non-response when planning your actual outreach. Divide the required sample size by your expected response rate to determine how many people to contact.

Sample Size Formula

Variables Explained

• n: The required sample size assuming an infinite population.
• z: The z-critical value corresponding to the chosen confidence level (e.g., 1.96 for 95%).
• p: The expected population proportion (as a decimal). Use 0.50 when unknown.
• E: The desired margin of error (as a decimal). For ±5%, E = 0.05.
• N: The total population size (for finite population correction).
• n_adj: The adjusted sample size after applying finite population correction.

Step-by-Step Example

A company wants to survey employees about workplace satisfaction. There are 5,000 employees total. They want 95% confidence with ±4% margin of error. Expected proportion is unknown.

1. Set parameters: z = 1.96, p = 0.50 (unknown), E = 0.04, N = 5,000
2. Calculate infinite population n: n = (1.96² × 0.50 × 0.50) / 0.04² = (3.8416 × 0.25) / 0.0016 = 600.25 → 601
3. Apply finite population correction: n_adj = 601 / (1 + (601-1)/5000) = 601 / 1.12 = 536.61 → 537

The company needs to survey at least 537 employees out of 5,000 to achieve ±4% precision at 95% confidence. The finite population correction reduced the requirement from 601 to 537 (an 11% reduction). If the expected response rate is 75%, they should invite 537 / 0.75 = 716 employees to participate.

Practical Examples

Example 1: Maria's Market Research Survey

Maria is launching a new product and wants to survey potential customers about purchase intent. She targets the general population (effectively infinite) and wants 95% confidence with ±3% margin of error. Based on pilot testing, she expects about 40% interest.

• z = 1.96, p = 0.40, E = 0.03, N = infinite
• n = (1.96² × 0.40 × 0.60) / 0.03² = (3.8416 × 0.24) / 0.0009 = 1,024
• With expected 25% online response rate: 1,024 / 0.25 = 4,096 invitations needed

Maria needs at least 1,024 completed responses. Using p = 0.40 instead of 0.50 actually reduces the requirement slightly (from 1,068 with p = 0.50) because 0.40 × 0.60 = 0.24 is less than 0.50 × 0.50 = 0.25. She plans to send 4,100 email invitations to account for the low response rate typical of online surveys.

Example 2: Dr. Ahmed's Clinical Study Planning

Dr. Ahmed is planning a clinical study to estimate the prevalence of a health condition in a city of 250,000 adults. He needs 99% confidence with ±2% precision. Previous studies suggest the prevalence is approximately 15%.

• z = 2.576, p = 0.15, E = 0.02, N = 250,000
• n = (2.576² × 0.15 × 0.85) / 0.02² = (6.6358 × 0.1275) / 0.0004 = 2,115
• With FPC: 2,115 / (1 + 2,114/250,000) = 2,115 / 1.00846 = 2,097

The finite population correction saves only 18 participants because the population of 250,000 is much larger than the sample. Dr. Ahmed needs approximately 2,097 participants. At the stricter 99% confidence level, the sample is about 80% larger than it would be at 95% confidence (about 1,225). He budgets for 2,800 recruitment contacts assuming a 75% participation rate in clinical studies.

Example 3: Jake's School District Assessment

Jake manages a school district with 3,200 students and needs to survey student satisfaction. He wants 90% confidence with ±5% margin of error. He has no prior data on satisfaction levels.

• z = 1.645, p = 0.50, E = 0.05, N = 3,200
• n = (1.645² × 0.50 × 0.50) / 0.05² = (2.706 × 0.25) / 0.0025 = 271
• With FPC: 271 / (1 + 270/3,200) = 271 / 1.0844 = 250

Jake needs responses from only 250 students out of 3,200 (about 7.8% of the population). The FPC saves 21 responses because the sample is a meaningful fraction of the population. At the more relaxed 90% confidence level, the sample is considerably smaller than what 95% would require (384 without FPC). This is a practical choice for a school district where resources are limited. For detailed analysis of the results, Jake can use our confidence interval calculator.

Sample Size Reference Table

Values assume p = 0.50 (most conservative) and infinite population.

Tips and Complete Guide

Planning for Non-Response

Non-response is inevitable in any survey. Plan for it by dividing your required sample size by the expected response rate: Outreach = n / Response Rate. For mail surveys, expect 20-40% response; for email, 10-30%; for phone, 40-60%; for in-person, 60-80%. Non-response can also introduce bias if those who do not respond differ systematically from those who do. Consider follow-up contacts and incentives to improve response rates and reduce non-response bias.

When to Use This Formula vs. Power Analysis

The formula on this page calculates sample size for estimating a proportion or mean with a specified margin of error. For comparing groups (e.g., does treatment A differ from treatment B?), you need a power analysis, which also considers effect size and statistical power. Power analysis is more complex and depends on the specific statistical test you plan to use. The margin-of-error approach is ideal for descriptive studies, surveys, and polls.

Budget and Practical Constraints

Sample size calculations give you the statistically required minimum, but real-world constraints often dictate the actual sample. If the calculated size exceeds your budget, consider widening the margin of error, reducing the confidence level, or narrowing the population. You can also use stratified sampling to improve precision without increasing sample size. Always be transparent in your report about the achieved precision and any compromises made due to practical limitations.

Common Mistakes to Avoid

• Forgetting to account for non-response: The calculator gives the number of completed responses needed. If your response rate is 50%, you need to contact twice as many people. Failure to account for non-response is the most common practical mistake in survey planning.
• Using the wrong formula type: This formula is for estimating proportions (yes/no questions, satisfaction ratings). If you are estimating a mean with known standard deviation, the formula changes to n = (z × σ / E)². Mixing up these formulas leads to incorrect sample sizes.
• Assuming 50% proportion when you have better information: Using 50% is conservative but may overestimate the needed sample. If prior research or a pilot study gives you a reasonable proportion estimate, use it. The savings can be substantial: at p = 0.10, you need only 60% of the sample required at p = 0.50.
• Ignoring stratification or clustering: If your sampling design uses clusters (e.g., surveying entire classrooms rather than individual students), you need a design effect multiplier, typically 1.5 to 3.0, increasing the required sample size proportionally.
• Not rounding up: Always round the sample size UP to the nearest whole number. Rounding down means you do not quite reach your desired precision. Our calculator handles this automatically.

Frequently Asked Questions