How to Calculate Sample Size for Surveys
Quick Answer
Sample size formula: n = (Z² × p × (1 - p)) ÷ e²
- Z = z-score for confidence level (95% confidence: Z = 1.96)
- p = estimated proportion (use 0.5 if unknown)
- e = margin of error (e.g. 0.05 for ±5%)
For 95% confidence, ±5% margin of error, unknown proportion:
n = (1.96² × 0.5 × 0.5) ÷ 0.05² = 384 participants
Choosing the right sample size is one of the most important steps in survey design. Too small a sample gives unreliable results. Too large wastes resources. Use the free Sample Size Calculator on CalConvs for instant results.
The Key Inputs to Sample Size Calculation
- Confidence level: How certain you want to be that the true population value lies within your margin of error. Common choices: 90%, 95%, 99%.
- Margin of error (e): The maximum acceptable difference between your sample result and the true population value. Common choices: ±3%, ±5%, ±10%.
- Expected proportion (p): Your best estimate of the prevalence you are measuring. If unknown, use 0.5 (most conservative, gives largest sample).
- Population size (N): Only matters when population is small (under 10,000).
Sample Size Reference Table (p = 0.5)
| Parameters | Required Sample Size | When to Use |
|---|---|---|
| 95% confidence, ±10% margin | 96 | Very small study. High uncertainty. |
| 95% confidence, ±5% margin | 384 | Standard for most surveys. |
| 95% confidence, ±3% margin | 1,067 | Needed for accurate polling. |
| 95% confidence, ±2% margin | 2,401 | National opinion polls. |
| 95% confidence, ±1% margin | 9,604 | Very precise national survey. |
| 99% confidence, ±5% margin | 664 | Higher certainty, larger sample needed. |
| 90% confidence, ±5% margin | 271 | Acceptable for exploratory research. |
How to Adjust for Small Populations
Finite Population Correction: Adjusted n = n ÷ (1 + (n - 1) ÷ N)
Example: Initial sample size n = 384. Population N = 800.
Adjusted n = 384 ÷ (1 + (384 - 1) ÷ 800) = 384 ÷ 1.479 = 260 participants.
When N is very large (over 100,000), this correction makes almost no difference.
Practical Sample Sizes for Common Research Contexts
| Research Type | Typical Sample Size |
|---|---|
| Customer satisfaction survey (small business) | 50 to 100 responses |
| Market research for a product launch | 300 to 500 responses |
| National opinion poll (UK, US) | 1,000 to 2,000 responses |
| Academic dissertation survey | 100 to 400 responses |
| Clinical trial (Phase II) | 50 to 300 participants |
| A/B test on a website | 1,000 to 10,000 per variant |
Sample Size and Research by Country
- United Kingdom: Market Research Society guidelines. Major polls use 1,000 to 2,000 respondents.
- United States: AAPOR standards. National polls use 800 to 1,500 respondents.
- India: MRSI standards. Large diverse population means larger samples needed for regional representativeness.
- Australia: AMSRO standards. Australian Bureau of Statistics provides population data for sampling frames.
Frequently Asked Questions
How many people do I need to survey to get reliable results?
For a general population survey with 95% confidence and ±5% margin of error, you need approximately 384 respondents. Use the Sample Size Calculator on CalConvs to find the exact number for your specific confidence level and margin of error.
Does a larger population need a larger sample?
Not significantly. A sample of 384 provides the same accuracy for a country of 1 million as it does for a country of 1 billion, provided the sample is truly random. Sample size is determined by the required accuracy (margin of error), not the population size.
What is statistical power and how does it relate to sample size?
Statistical power is the probability that a test will detect an effect if one truly exists. Higher power requires larger samples. Power of 0.80 (80%) is the standard minimum for most academic research.
Related Tools
- Sample Size Calculator: instant sample size for your confidence level and margin
- Confidence Interval Calculator: build intervals around your survey results
- Z-Score Calculator: standardise values for significance testing
- All Math Tools: 46 tools on CalConvs