In order to keep themselves going in the absence of sunlight, plants perform division equations throughout the night to ration their stores of starch until the moment the sun reappears.
By counting their starch and dividing it by the number of hours left until morning they ensure they do not run out until the crack of dawn, and can even adjust their calculations during the night.
The discovery is the first known example in nature of sophisticated arithmetic being carried out at a fundamental level, as opposed to in the brain cells of animals like humans, scientists said.
It plays a crucial role in plants' survival because they are dependent on starch, which is produced from carbon dioxide and sunlight during the day, to provide energy during the night.
If they were to find themselves without starch during the hours of darkness they would quickly begin to starve, would stop growing and take several hours to recover even after light returned.
"The capacity to perform arithmetic calculation is vital for plant growth and productivity," Prof Alison Smith, a metabolic biologist who helped make the discovery, explained.
"The calculations are precise so that plants prevent starvation but also make the most efficient use of their food. If the starch store is used too fast, plants will starve and stop growing during the night. If the store is used too slowly, some of it will be wasted."
It was already understood that plants have a mechanism which ensures their starch is not used up until the end of the night, but scientists previously had no idea how they managed it.
Researchers from the John Innes Centre in Norwich discovered the hidden ability after studying Arabidopsis, a small flowering plant in the mustard family.
They found that the plants used their starch at a steady rate throughout the night, so that about 95 per cent of their stock had been used up by dawn each day.
When researchers changed light conditions to make night arrive unexpectedly early or late, the plants adapted by slowing or increasing their rate of starch usage to ensure their reserves lasted until dawn.
This indicated that they had made a new calculation based on their internal clock which knows the amount of time left until morning, Prof Smith explained.
When the plants' light exposure was shortened so that they had a smaller batch of starch to begin with, they consumed it more slowly, demonstrating that the equation could also change based on the size of their reserves.
The scientists even attempted to trick the plants by introducing windows of sunlight during the night but each time they were able to adjust their starch use accordingly, demonstrating that the balance was being continuously computed throughout the night.
They suggested that information about the size of the plants' starch stores and the time left until dawn must be based on the levels of two types of molecules, dubbed "S" for starch and "T" for time.
"We propose there is a molecule called S which tracks the amount of starch in the plant, and a molecule called T which tracks the time until dawn," Prof Smith explained. "The closer to dawn you get, the less of T and S you have."
If the "S" molecule prompts the use of starch and the "T" molecule prevents it, then dividing the number of "S" molecules by "T" molecules would enable the plant to use up its reserves at a steady rate and expire at dawn, she explained.
Professor Martin Howard, who came up with the equation, said the study provides "The first concrete example in biology of such a sophisticated arithmetic calculation" at a fundamental biological level.
But similar equations could be responsible for other natural phenomena where reserves are built up ahead of long periods without food, and run out just as the period of fasting ends.
Migrating little stints arrive at their Arctic breeding grounds following a 5,000km journey with fat reserves so low that they could only survive another 14 hours, they wrote in the eLife journal.
Similarly, during the four-month period in which they incubate eggs, male emperor penguins' fat levels reach a critically low level just at the point their partner is expected to return.