Survey sample-size calculator

See what each point of precision costs.

Try the calculator

What the film shows, in words

See what each point of precision costs.
12,000 people. ±5% at 95% confidence. 373 answers. Invite 622.
A hundred times more people. 385 answers. Twelve more.
Ask for ±3%: 1,067 answers.
If 40% reply: invite 2,668.
Choose the precision. Then plan the fieldwork.

The demo: the worked example, one input at a time

ExampleStep 1 of 5A staff survey in an organisation of 12,000 people (illustrative figures).

12,000 staff. ±5%. 373 answers.

SelectionRandom

Confidence95%

Expected proportion50%

Margin of error±5%45% to 55%

Population12,000people

±10%96±7%193±5%373±4%572±3%98155%45%±5.0% at 95% confidencecloses at 12,000

05001,0001,5002,0002,5003,000

622 invited

373

373completed responses

622people to invite at a 60% response rate

±5.0%margin at 95% confidence

Response rate60%Of 622 invited, 373 answer and 249 do not.

The jaws stand at 45% and 55%. The cut falls where the horn first fits between them.

n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16. n = 384.16 ÷ (1 + 383.16 ÷ 12,000) = 372.27, rounded up: 373. Invitations: 373 ÷ 0.60 = 621.67, rounded up: 622.

Now your survey. Set the jaws.

Live

±10%96±7%193±5%373±4%572±3%98155%45%±5.0% at 95% confidencecloses at 12,000

05001,0001,5002,0002,5003,000

622 invited

373

373completed responses

622people to invite at a 60% response rate

±5.0%margin at 95% confidence

Confidence level

90%95%99%

Expected proportion

If you do not know, keep 50%: it gives the largest, safest sample.

Margin of error

±%

A result of 50% would mean between 45% and 55%, at 95% confidence.

Population size

people

Everyone the result should describe, for example all staff or all registered members.

Expected response rate

percent %

Of 622 invited, 373 answer and 249 do not.

How will people be selected?

RandomStratified randomClusterConvenience or opt-in

Design effect

1.0 for simple random samples. Clustered samples often need more; your statistician can estimate it.

Subgroups needing their own estimate

For example 3 if each region must be reported separately at the same precision.

Response is rarely random. People who answer differ from those who do not. Plan follow-ups and compare respondents with known population figures.

The full result

Work out how many completed responses you need, and how many people to invite, for a survey estimate at the precision you choose. The formula and its limits are on the page.

373completed responses needed

622people to inviteat a 60% response rate

±5.0%margin at 95% confidencefor one proportion

How precision improves with more responses (margin of error, ±%)

95% confidence, p = 50%

Alternatives at the same confidence

Margin of error	Completed responses	Invitations
±3%	981	1,635
±4%	572	954
±5%	373	622
±7%	193	322
±10%	96	160

Read before you field the survey

Check: Response is rarely random.People who answer differ from those who do not. Plan follow-ups and compare respondents with known population figures.

Your full reportSample-size worksheetTry this form

Practice 01: Research, evidence & evaluationFree · instant results on this pageTool owner: Michael Gagakuma and Prof. Wisdom GagakumaVersion 1.0 · 24 September 2026

GKM Strategic Advisory & AI

Sample-size worksheet

Your organisation

±10%96±7%193±5%373±4%572±3%98155%45%±5.0% at 95% confidencecloses at 12,000

05001,0001,5002,0002,5003,000

622 invited

373

Completed responses: 373
Invitations: 622
Precision: ±5.0% at 95%

Alternatives at the same confidence
±3%	981 responses	1,635 invitations
±4%	572 responses	954 invitations
±5%	373 responses	622 invitations
±7%	193 responses	322 invitations
±10%	96 responses	160 invitations

PDF · 24 September 2026

The first page as it stands, with your horn and the figures above. It changes as you change the inputs.

Your full report

Sample-size worksheet, by email once delivery is connected.

Your assumptions
The formula used
The non-probability warning
A fieldwork planning checklist

· a free brief, or book Michael · from USD 90

Tool: Survey sample-size planner
Population: 12,000; selection: random; 95% confidence; ±5%
Result: 373 responses · 622 invitations
Request: please review the sampling plan and fieldwork approach.

Send as a brief

The passage square on: two concrete walls stand apart, and the tall sapphire glass blade stands between them with an even gap of daylight on each side, the sea beyond. — The blade is the estimate. The gap on each side is the plus and the minus of the margin, and it never closes.

How it is worked out, and its limits.

The formula is published so you can check it. Every count on this page comes from it.

Method

01
Initial size: n₀ = z² × p(1 − p) ÷ e², where z is 1.645, 1.960 or 2.576 for 90%, 95% or 99% confidence, p is the expected proportion and e the margin of error.
02
Finite population correction: n = n₀ ÷ (1 + (n₀ − 1) ÷ N), applied to each subgroup, then multiplied by the design effect.
03
Invitations = completed responses ÷ expected response rate, rounded up.
04
Check value: N = 12,000, 95% confidence, ±5%, p = 50% gives 373 completed responses.

What it cannot tell you

Margins of error apply only to probability samples.
It sizes the estimate of one proportion. Comparing groups or testing a change needs a power calculation.
It cannot correct for non-response bias or poorly worded questions.

Quality ruleKnown formula fixtures; reject impossible proportions.

From inside the passage, beside the tall sapphire glass pane, looking out of its wide mouth onto a stone terrace of large square pavers, with the sea and a headland beyond.

The number is the start. Then comes the fieldwork.

A sample size says how many answers you need. Who is asked, how they are reached and what is done about those who stay silent decide whether the answers can be trusted.