Blink-Free Group Photo Calculator

Background.

In 2006 Nic Svenson, a science writer at CSIRO, asked physicist Piers Barnes a question every photographer has muttered under their breath: how many photographs of a group do you have to take before you get one where nobody is blinking? Barnes's reply — "You don't need data, we can model it" — turned into a short paper, "Blink-Free Photos, Guaranteed", and an Ig Nobel Prize in Mathematics for calculating "the number of photographs you must take to (almost) ensure that nobody in a group photo will have their eyes closed". This calculator implements that model.

The arithmetic is three lines. The chance that any one person is mid-blink when the shutter opens is their blink rate multiplied by the window in which a blink would spoil the frame — the eyelid closure time plus the exposure time. The chance a whole frame is clean is that miss-probability raised to the number of faces. And the chance that at least one of several frames is clean is one minus the chance that all of them fail. Invert the last line and you get the number of frames you need for whatever confidence you can live with.

What makes the result surprising is the exponent. At a rest-state blink rate of 17 blinks a minute and a 0.3-second spoil window, one person ruins a frame about 8.7 % of the time — which sounds negligible until you raise 0.913 to the twelfth power and discover that a group of twelve produces a usable frame only a third of the time. Every extra guest multiplies your odds by 0.913 again.

The honest caveat comes from Barnes himself: "We are proud to have made a gross simplification of complex physiological and psychological factors backed up with no empirical data." Real groups blink in loose synchrony, flashes provoke reflex blinks, and blink rate swings with conversation, tiredness, contact lenses and air conditioning. Every physiological number here is therefore an input rather than a hidden constant, with defaults taken from published measurements, so you can tune the model to the room you are standing in.

What is blink-free group photo calculator?

The blink-free photo problem is a small exercise in independent Bernoulli trials dressed up as a practical question. Each person in each frame is a trial that succeeds if their eyes are open; the frame succeeds only if every trial in it succeeds; and the shoot succeeds if any frame succeeds. The physiology enters in one place: converting a blink rate into a per-frame probability. Blinking is roughly a Poisson process, so the expected number of blinks in a short window of length T is simply rate × T, and for small values that expectation doubles as the probability of at least one blink. The window is not the exposure time alone — a blink that starts a tenth of a second before the shutter opens still has the eyes shut when it does — so the spoilable window is the eyelid closure duration plus the exposure. Published measurements put spontaneous blink rate at about 17 per minute at rest, rising to 26 in conversation and falling to 4.5 while reading, and a complete eyeblink at somewhere between 75 and 400 milliseconds. Those ranges, not single values, are the honest inputs, which is why this page exposes all of them. The model's most consequential simplification is independence between people. Groups synchronise: a countdown, a flash, or a joke propagates through a line-up, so the real distribution of clean frames is more clustered than the binomial says. It also has nothing to say about the person who blinks precisely because a flash went off. Treat the output as a well-posed lower bound on the number of frames rather than a promise.

How to use this calculator.

1. 01Count the faces that have to have their eyes open and enter that number. It is the exponent in the model, so it matters more than anything else on the page.
2. 02Pick a blink rate. 17 blinks a minute is the measured resting average; use 26 if people are chatting, and lower it towards 5 if the group is concentrating on something.
3. 03Leave the spoil window at 0.3 seconds unless you have a reason not to. Measured blinks run 0.075 to 0.4 seconds, and 0.3 is a deliberately unforgiving choice because a half-open eye is as bad as a closed one in a printed portrait.
4. 04Enter your shutter time. In good light at 1/125 s the exposure adds almost nothing; at 1/15 s in a dim hall it adds a fifth to the spoil window, which is exactly why the original rule of thumb distinguishes good light from bad.
5. 05Choose a confidence and read the shot count — then read the rule-of-thumb line underneath, which shows what the original published rule would have told you and where the two diverge.
6. 06Take the frames with real gaps between them, not as one burst. Frames milliseconds apart are not independent trials, and the model assumes they are.
7. 07Then ignore the number and take a couple more anyway, because somebody will have moved.

The formula.

Start with one person. Blinking is close enough to a Poisson process that the expected number of blinks in a window of length T is rate × T, and for the small windows involved here that expectation is also the probability of at least one blink. The window is the eyelid closure duration w plus the exposure time t, because a blink that begins shortly before the shutter opens still has the eyes shut when it does:

p = r × (w + t)

At the defaults, r = 17/60 = 0.2833 blinks per second, w = 0.3 s and t = 1/125 s = 0.008 s, so p = 0.2833 × 0.308 = 0.0873, or 8.73 %.

Now the frame. Treating people as independent — the model's biggest simplification, and one worth remembering — the chance nobody in a group of n is blinking is

P₁ = (1 − p)ⁿ

For twelve people that is 0.9127¹² = 0.3343. Only a third of frames are usable. The exponent is what makes this counter-intuitive: the per-person risk is small, but it compounds.

Finally the shoot. Frames are independent trials, so the chance that all k of them fail is (1 − P₁)ᵏ and the chance at least one succeeds is

P(k) = 1 − (1 − P₁)ᵏ

Invert for a target confidence c and round up, because part-frames do not exist:

k = ⌈ ln(1 − c) / ln(1 − P₁) ⌉

At 99 % confidence with twelve people, k = ⌈11.32⌉ = 12 frames, which then delivers 99.24 %. The expected number of frames before the first clean one is just 1 ÷ P₁ = 2.99 — much smaller than 12, and the gap between those two numbers is the whole reason for the calculation. "On average three frames" is not the same as "three frames will do it".

What the model does not include: correlation between people, which is real and substantial — countdowns and flashes synchronise blinking; reflex blinking caused by the flash itself; the fact that burst-mode frames milliseconds apart are nearly the same trial repeated; and any of the reasons a group photo actually fails, such as somebody looking away, a child turning round, or the tall one at the back closing their eyes deliberately.

A worked example.

Frequently asked questions.

References& sources.

1. [1]CSIRO (2006). 'CSIRO boasts Ig Nobel laureates' — news release. Source of the published rule of thumb, quoted verbatim: 'for groups of less than 20, you divide the number of people by three if there's good light or a decent flash, and two if the light's bad', and of Dr Piers Barnes's own caveat: 'We are proud to have made a gross simplification of complex physiological and psychological factors backed up with no empirical data.'
2. [2]Improbable Research. 'In short, how to take a group photo with no blinks', and the 2006 Ig Nobel Prize citation. Confirms the award to Nic Svenson and Piers Barnes of CSIRO 'for calculating the number of photographs you must take to (almost) ensure that nobody in a group photo will have their eyes closed', and the original publication: Nic Svenson and Piers Barnes, 'Blink-Free Photos, Guaranteed', Velocity, June 2006.
3. [3]Bentivoglio, A. R., Bressman, S. B., Cassetta, E., Carretta, D., Tonali, P. & Albanese, A. (1997). 'Analysis of blink rate patterns in normal subjects.' Movement Disorders 12(6): 1028–1034. 150 healthy volunteers (70 male, 80 female; aged 35.9 ± 17.9 years, range 5–87) videotaped at rest, reading and talking: 'Mean BR at rest was 17 blinks/min, during conversation it increased to 26, and it was as low as 4.5 while reading.' Source of the blink-rate default and of the three options offered in the field hint.
4. [4]Alsaeedi, N. & Wloka, D. (2019). 'Real-Time Eyeblink Detector and Eye State Classifier for Virtual Reality (VR) Headsets (Head-Mounted Displays, HMDs).' Sensors 19(5): 1121, doi:10.3390/s19051121. States that 'each eyeblink can last between 75 and 400 ms', and tabulates spontaneous-blink kinematics from Bologna et al. — closing duration 71.5 ± 4.7 ms, fully-closed pause 13.7 ± 3.3 ms. Source of the eyelid-closure window default and of the range quoted in the field hint.