ELi5: Decades ago when countries were still testing nuclear bombs sometimes the scientists incorrectly predicted how large the explosions would be. How did they accurately calculate the actual size of the explosions after the fact?

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Atomic tests were generally monitored with instruments to measure the yield. Here are a few ways it was measured:

1. Size of the fireball. The more powerful the bomb, the larger the fireball. Using a high speed movie camera, they could record the fireball and figure out how large it got.

2. Measure the wind/shockwave. Nuclear blasts put out a powerful wave of air pressure. If you measure the pressure at a known distance, you can figure out how powerful an explosion caused it.

3. Measure how much the ground shakes. Just like with the air, there is a pressure wave that travels through the ground. Using seismometers, the amount of ground shake can be used to calculate the size of the explosion. This can be done from very far away, and is used to calculate how large atomic tests done by other countries are (like the US monitoring North Korean nuclear tests).

4. Radiation measurements. Atomic bombs create a quick intense burst of radiation, then a cloud of radioactive particles (fallout). These can both be measured and used to estimate the nuclear yield.

Generally all four of these methods would be used, and by combining the estimates of all of them, you could get a fairly good idea of how large the blast was. It isn’t 100% precise, which is why you often see a fairly round number (10 kilotons instead of 9.734 kilotons).

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