Sample Size Calculator

Determine the required statistically valid sample size for surveys and research experiments with customizable confidence levels, margins of error, and finite population correction.

Sample Parameters

Live calculation
Preset Scenarios:

Sample sizes are always rounded UP to the nearest integer to guarantee target statistical power.

Recommended Sample Size (n)
385respondents
Target Confidence Level95% (z=1.96)
Population: Infinite / UnknownUnadjusted n₀: 384.2
Margin of Error±5%
Critical Z-Value1.96
Assumed Variancep = 50%
FPC ReductionNone

Non-Response & Dropout Buffer Planning

Expected Response RateDropout BufferTotal Invitations Needed
100%None385 invites
80%+20% dropouts482 invites
50%+50% dropouts770 invites
30%Low response (Cold email)1,284 invites

How Sample Size Is Determined

Statistical sample size calculations determine the exact number of completed responses or experimental subjects required to estimate a population parameter within a specified margin of error (E) at a chosen confidence level.

1. Cochran's Formula for Proportions (Infinite Universe)
n₀=
z² × p(1 − p)E²
2. Finite Population Correction (FPC for Known N)
n=
n₀ × Nn₀ + (N − 1)
Step-by-Step Calculation Breakdown (Example: 95% Confidence, MOE = ±5%, p = 50%)
Step 1: Identify Critical Value (z*) and Maximum Variance
• For 95% confidence, z = 1.960 (z² = 3.8416)
• Variance numerator p(1 − p) = 0.50 × 0.50 = 0.250
Step 2: Compute Cochran's Initial Sample Size (n₀)
• Margin of Error E = 5% = 0.05 (E² = 0.0025)
• n₀ = (3.8416 × 0.25) ÷ 0.0025 = 0.9604 ÷ 0.0025 = 384.16
Step 3: Round Up to Whole Integer
• Required Sample Size = ⌈384.16⌉ = 385 respondents

Key Considerations in Study Planning

  • Non-Response Inflation: Always invite more participants than your minimum calculated sample size to compensate for dropouts and invalid surveys.
  • Conservative Variance: Keeping p = 50% guarantees the required statistical accuracy even if observed opinions deviate.

Frequently Asked Questions

Why does sample size matter so much in survey research?
Sample size dictates statistical power, precision, and confidence. An undersized sample produces wide margins of error and inconclusive results, whereas an oversized sample wastes budget and time. Pre-determining sample size guarantees your findings achieve desired statistical validity.
What is the Finite Population Correction (FPC)?
Finite population correction adjusts the required sample size downward when your sample constitutes a substantial portion (typically > 5%) of a known finite population. For instance, surveying 300 employees from a 500-person firm requires fewer participants than surveying 300 people from an infinite national universe.
Why is 50% used as the default expected proportion?
When the population proportion is completely unknown, p = 0.50 (50%) represents the worst-case scenario with maximum variance (p × (1 − p) = 0.25). This ensures your sample size is sufficiently conservative to meet your margin of error requirement regardless of the actual outcome.
How does confidence level affect sample size?
Demanding higher certainty increases the critical z-score (e.g. 1.96 at 95% vs 2.576 at 99%), quadratically increasing the necessary sample count.
How do I account for non-response rates?
If you anticipate a 20% non-response or dropout rate, divide your target sample size by 0.80. For example, if you need n = 385 completed surveys, you should invite 385 ÷ 0.80 = 482 participants.
Can I calculate sample size for continuous averages (means)?
Yes. In Mean Mode, enter your target margin of error in raw measurement units (E) alongside the expected population standard deviation (σ).

Related Tools