Calculator Servicescalculatorservices.com
Statistics

Sample Size Calculator

n = (zσ/ME)². Free online Sample Size Calculator. Calculate sample size online — fast, accurate, mobile-friendly, no signup needed.

Sample size
97

Derivation

  1. ├── 01Givenz = 1.96, sigma = 10, ME = 2
  2. ├── 02Formulaceil((t × a / n)^(2))
  3. └── 03Compute Sample size97
Did you know?

Every calculator here runs 100% in your browser — nothing is sent to a server or stored in a database.

§01What is

Understanding the Sample Size Calculator

The Sample Size Calculator computes Sample size from 3 inputs: z, σ, me. n = (zσ/ME)².

Statistics is how we make sense of noisy real-world data. Whether you’re analysing survey results, sports scores, or business metrics, a statistics calculator gives you the exact formula-based answer so you can focus on the interpretation. The Sample Size Calculator sits in that toolkit — it n = (zσ/ME)². Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

ceil((t × a / n)^(2))

Where

z
z
sigma
σ
ME
ME
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: z = 1.96, σ = 10, ME = 2.

  1. 01Start by noting the input — z: 1.96.
  2. 02Start by noting the input — σ: 10.
  3. 03Start by noting the input — ME: 2.
  4. 04Substitute these values into the formula: ceil((t × a / n)^(2))
  5. 05Compute Sample size: the calculator returns 97.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Sample Size Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

z halved

z = 0.98 (from 1.96)

Keep every other input at its default and halve the z. See how sample size responds.

  1. 01New z: 0.98
  2. 02Baseline Sample size: 97
  3. 03New Sample size: 25
  4. 04Sample size decreases by 74.2% → use this sensitivity to plan for real-world variation.
02 · PATTERN

z doubled

z = 3.92 (from 1.96)

Keep every other input at its default and double the z. See how sample size responds.

  1. 01New z: 3.92
  2. 02Baseline Sample size: 97
  3. 03New Sample size: 385
  4. 04Sample size increases by 296.9% → use this sensitivity to plan for real-world variation.
03 · PATTERN

σ halved

sigma = 5 (from 10)

Keep every other input at its default and halve the σ. See how sample size responds.

  1. 01New σ: 5
  2. 02Baseline Sample size: 97
  3. 03New Sample size: 25
  4. 04Sample size decreases by 74.2% → use this sensitivity to plan for real-world variation.
04 · PATTERN

σ doubled

sigma = 20 (from 10)

Keep every other input at its default and double the σ. See how sample size responds.

  1. 01New σ: 20
  2. 02Baseline Sample size: 97
  3. 03New Sample size: 385
  4. 04Sample size increases by 296.9% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
Your feedback

How useful was this calculator?

Your ratings stay in your browser — they help us learn which tools people actually rely on.

Rate it
Was this helpful?