What is the NNT?

Type how many people had the outcome in a control group and a treated group, or the two event rates. The NNT calculator gives the number needed to treat for one fewer bad outcome (or, for a harm, one more), with the absolute and relative risk reduction.

Number needed to treat: 10

The number needed to treat is 10 (NNTB, a benefit).

Rounded up to whole people: 10
Benefit or harm: NNTB, a benefit
Control event rate: 20%
Treated event rate: 10%
Absolute risk reduction: 10%
Relative risk reduction: 50%
Relative risk: 0.5

Number needed to treat: 10. The number needed to treat is 10 (NNTB, a benefit).

How to calculate

Computes the number needed to treat (NNT = 1 ÷ absolute risk reduction) from event counts or event rates in a control and a treated group, with the relative risk reduction.

Example with the default inputs (I have Event counts, Control group: events 20, Control group: people 100, Treated group: events 10, Treated group: people 100): The number needed to treat is 10 (NNTB, a benefit).

Method: CER = control events ÷ control group; EER = treated events ÷ treated group; ARR = CER − EER; NNT = 1 ÷ |ARR| (NNTB when ARR > 0, NNTH when ARR < 0); RRR = ARR ÷ CER; RR = EER ÷ CER.

The events are bad outcomes (deaths, strokes), so a lower rate in the treated group is a benefit.
Both groups are followed for the same length of time; the NNT applies to that time.
Rounding up to whole people is a page choice; the exact NNT is shown too.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

I have Event counts, Control group: events 20, Control group: people 100, Treated group: events 10, Treated group: people 100 gives Number needed to treat 10, Rounded up to whole people 10, Absolute risk reduction 10%, Relative risk reduction 50%, Relative risk 0.5.Source: https://pmc.ncbi.nlm.nih.gov/articles/PMC1114210/
I have Event rates, Control event rate (CER) 10%, Treated event rate (EER) 18% gives Number needed to treat 12.5, Rounded up to whole people 13, Absolute risk reduction -8%, Benefit or harm NNTH, a harm.Source: Altman DG. Confidence intervals for the number needed to treat. BMJ 1998;317:1309 (Tramèr et al.’s ARR of −0.08 gives an NNT of −12.5, an NNTH of 12.5; Altman gives no event rates, so 10% and 18% are example rates with that ARR); https://pmc.ncbi.nlm.nih.gov/articles/PMC1114210/
I have Event counts, Control group: events 15, Control group: people 120, Treated group: events 9, Treated group: people 130 gives Number needed to treat 17.931034, Rounded up to whole people 18, Control event rate 12.5%.Source: https://pmc.ncbi.nlm.nih.gov/articles/PMC1114210/

How it works

The outcome is a bad event (a death, a stroke, a relapse), counted in a control group and a treated group followed for the same time.

Control event rate (CER) = control events ÷ people in the control group. Treated event rate (EER) = treated events ÷ people in the treated group. In "Event rates" mode you type both as percents (0 to 100), and the page divides by 100.
Absolute risk reduction (ARR) = CER − EER. It is shown in percentage points and is negative when the treated group does worse.
Number needed to treat = 1 ÷ |ARR| (with ARR as a fraction, not a percent). When ARR > 0 it is an NNTB (benefit); when ARR < 0 it is an NNTH (harm), as Altman (1998) suggests. The "Benefit or harm" row reads NNTB, a benefit or NNTH, a harm.
Rounded up: the NNT rounded up to the next whole number (17.93 becomes 18; exactly 10 stays 10).
Relative risk reduction (RRR) = ARR ÷ CER, in percent. Relative risk (RR) = EER ÷ CER. Both are left out when CER is 0, or when RR would be over 10¹⁵.

Rules. Counts are whole numbers; each group has at least 1 person, and events cannot be more than people. When ARR is 0 there is no answer (the NNT is infinite), and when the NNT would be over 10¹² (a trillion) people there is no answer either.

Rounding. Every value is an exact fraction of the typed numbers, rounded once for display: the NNT to 1 decimal, rates and reductions to 2 decimals, RR to 3 decimals. The page gives point values only, not confidence intervals.

Worked examples by hand

ARR of 10 points (page default). Control 20 of 100, treated 10 of 100. CER = 20%, EER = 10%, ARR = 10 points = 0.10. NNT = 1 ÷ 0.10 = 10.0, rounded up 10, NNTB, a benefit. RRR = 10 ÷ 20 = 50.00%; RR = 10 ÷ 20 = 0.500.

A harm. CER = 10%, EER = 18% (typed as rates). ARR = 10 − 18 = −8.00 points = −0.08. NNT = 1 ÷ 0.08 = 12.5, rounded up 13, NNTH, a harm. The ARR of −0.08 comes from Altman (1998), who quotes Tramèr et al.'s trial of ondansetron and droperidol: an NNT of −12.5, which he writes as an NNTH of 12.5. Altman gives no event rates; 10% and 18% are example rates with that ARR.

Unequal groups. Control 15 of 120, treated 9 of 130. CER = 15 ÷ 120 = 12.50%; EER = 9 ÷ 130 = 6.923%. ARR = 0.125 − 0.0692308 = 0.0557692. NNT = 1 ÷ 0.0557692 = 17.9, rounded up 18.

Other questions people ask

How do I calculate NNT?

Subtract the treated event rate from the control event rate to get the absolute risk reduction (ARR), then take 1 ÷ ARR. If 20% of the control group and 10% of the treated group have the outcome, ARR = 0.10 and NNT = 1 ÷ 0.10 = 10.

What does an NNT of 10 mean?

On average, 10 people must be treated, for the length of the study, for one of them to avoid the bad outcome. The lower the NNT, the more effective the treatment; an NNT of 1 means every treated person benefits.

What is NNTH (number needed to harm)?

When the treated group has more bad outcomes than the control group, the ARR is negative. Altman (1998) suggests calling 1 ÷ |ARR| the number needed to treat for harm (NNTH): how many people treated lead to one extra bad outcome.

Why is the NNT rounded up?

You cannot treat part of a person, so the page also shows the NNT rounded up to the next whole number. The exact value is shown too; 17.93 becomes 18.

What is the difference between absolute and relative risk reduction?

The absolute risk reduction is the difference between the two event rates (20% − 10% = 10 points). The relative risk reduction divides that by the control rate (10 ÷ 20 = 50%). The same relative reduction gives a much larger NNT when the outcome is rare.

What if the two rates are equal?

Then the ARR is 0 and the NNT is infinite: the treatment makes no difference to the outcome in this data. The page gives no answer in that case.