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This month the laser at Magurele, Romania became the most powerful laser in the world, according to various sources.

Related: Is the laser built in Măgurele, România, the most powerful in the world?

Digi24, a Romanian news and television company mentioned:

Laserul Institutului de fizică nucleară de la Măgurele a atins cea mai mare putere din lume, echivalentă cu 10 procente din cea a Soarelui şi încă nu este la capacitatea maximă.

Translated:

The laser of the Nuclear Physics Institution at Magurele reaches the highest power in the world, equivalent with 10 percent of that of the Sun, and it’s not yet at its highest capacity.

Is that true? How did the scientists calculate that the laser is 10% of the power of the Sun?

It's possible they are actually talking about the rate of energy given off by the Sun that reaches the Earth. However, they are not talking about the amount of energy released, but rather the rate of energy released.

The "laser at Magurele, Romania" is actually part of the Extreme Light Infrastructure, a pan-European research project, described by Wikipedia as

...a laser facility that aims to host the most intense beamline system worldwide, develop new interdisciplinary research opportunities with light from these lasers and secondary radiation derived from them, and make them available to an international scientific user community.

According to the wikipedia article, on 13 March 2019, the ELI NP Research Centre, which is the facility located in Magurele, released a communication regarding the results of a demonstration test.

On March 13, 2019, Magurele held the public communication of the ELI-NP high-power laser system test results, which was also a demonstration test, confirming the achievement of the power of 10 [Petawatts].

A Petawatt is the equivalent of 1,000,000,000,000,000 (15 zeroes), or 10^15 Watts, as the prefix Peta describes. Therefore, a 10 Petawatt laser would be a 10x10^15, or 10^16 Watts.

Per this report from Sandia National Laboratories, they calculate the amount of solar energy that reaches the earth's surface as 89,300 Terawatts.

A Terawatt is the equivalent of 1,000,000,000,000 (12 zeroes) or 10^12 watts. A Petawatt is equal to 1,000 Terawatts, so you can easily convert between the two by dividing the number of Terawatts by 1,000 to get the number of Petawatts. Therefore, the amount of solar energy hitting the Earth in Petawatts is 89.3 Petawatts.

Dividing the output of the ELI-NP lazer test by the energy output of the Sun that reaches the surface of the Earth results in

10 Petawatts / 89.3 Petawatts = 11.198%

which is approximately 10%. Note however, that this does not mean that the laser is generating 10% of the sun's energy. Per the Wikipedia article on Watt

[The Watt] is defined as a derived unit of 1 joule per second,1 and is used to quantify the rate of energy transfer.

Further down, the page has a section on the distinction between "Watts" and "Watt-hours".

The terms power and energy are frequently confused. Power is the rate at which energy is generated or consumed and hence is measured in units (e.g. watts) that represent energy per unit time.

For example, when a light bulb with a power rating of 100W is turned on for one hour, the energy used is 100 watt hours (W·h), 0.1 kilowatt hour, or 360 kJ. This same amount of energy would light a 40-watt bulb for 2.5 hours, or a 50-watt bulb for 2 hours.

Power stations are rated using units of power, typically megawatts or gigawatts (for example, the Three Gorges Dam is rated at approximately 22 gigawatts). This reflects the maximum power output it can achieve at any point in time. A power station's annual energy output, however, would be recorded using units of energy (not power), typically gigawatt hours. Major energy production or consumption is often expressed as terawatt hours for a given period; often a calendar year or financial year. One terawatt hour of energy is equal to a sustained power delivery of one terawatt for one hour, or approximately 114 megawatts for a period of one year.

Typically, these kinds of experimental lasers are not constantly on, and fire for an extremely short period of time. Per the article on the National Ignition Facility, a facility with a similar, albeit less powerful laser

NIF aims to create a single 500 terawatt (TW) peak flash of light that reaches the target from numerous directions at the same time, within a few picoseconds.

A 10 Petawatt laser fired for a single picosecond would consume

10^16 Watts * (1 / 10^12) seconds = 10,000 Watt-seconds

10,000 Watt-seconds / 3,600 (seconds/hour) = 2.78 Watt-hours

Compare this number to the energy consumption of the world which was approximately 22 Terawatt-hours in 2017, and the amount of energy consumed by this laser is completely insignificant, accounting for less than a trillionth of the world's energy consumption.

Power of the laser

This video shows interviews with people at the laser center. At 4:54 you can see the director of the center repeat the claim. In this video, that same director states that the laser was measured at 10.88 PW or 1.088×10^16 W. Remember that watts (W) are the unit of power.

The laser does not operate at that power continuously. Just for comparison, that power is 30 million times the generating power of the whole EU. The laser stores up power and releases it in very short bursts. This document was written during the design phase, and said that they would try to make the laser do pulses of 22 fs or 2.2×10^-14 s, which is an incredibly short time. I don't know how long the pulses are in the laser as built, but we can assume they are incredibly short.

Power of the sun

The claim is that the sun's power is only ten times that of the laser. The "power of the sun" is a little vague. There are different ways to think about the sun's power.

The sun sends 3.846×10^26 W into space in all directions. That is 10^10 or 10,000,000,000 times more than the laser. Most of this energy just flies off into space, and does nothing. A minuscule fraction of that incredible power hits the Earth. Roughly 1.73×10^17 W hits the upper atmosphere. Of the power hitting the upper atmosphere, only 71% is absorbed by the Earth, 1.2×10^17 W. This is just 11 times the power of the laser, which is consistent with the claim.

In contrast to the laser, the sun provides that power 24/7, and spreads the energy out over the whole Earth.

Some calculations for context

If we go back to basic physics, power is energy per unit time. A huge amount of power sustained for a very brief amount of time, is a moderate amount of energy. 10.88 PW sustained for 22 fs is 240 J, enough energy to power a CFL lightbulb for 16 seconds; Not much energy on a everyday scale. However, if even a small amount of energy is concentrated into a tiny enough space, it can produce very high concentrations of energy. The laser is remarkable not just for its incredible power, but also because it can concentrate that power into a microscopic space, briefly creating incredible concentrations of energy.

Conclusion The laser produces roughly 10% of the power of the sunlight that is absorbed by the Earth. It produces that much energy for a tiny fraction of a second.