Hydroelectric Power Calculator

Linear in both flow and head, and 90 percent efficient because it dodges the Carnot limit.

Power output4.1678 MW4,167.8 kW

Annual generation16,430 MWhat a 45% capacity factor

Homes supplied4,694at about 3.5 MWh a year each

With double the flow8.336 MWexactly double — it is linear

With double the head8.336 MWalso exactly double

Hydraulic power before losses4.9033 MW

Lost to inefficiency0.7355 MW

Hydro turbines reach 90 to 95 per cent because they convert mechanical energy directly and are not bound by the Carnot limit that caps every heat engine. That is much of why hydro is still the largest renewable source worldwide.

The formula

P = rho * g * Q * H * efficiency

Linear in both, unlike wind

Hydroelectric power is proportional to the flow AND to the head, both to the first power. That is a very different engineering problem from wind: a small stream falling a long way can match a large river falling a little, and the choice between them is about terrain and civil works rather than about physics.

Efficiency is remarkably high

Large hydro turbines reach 90 to 95 %, far above any thermal plant, because they are not limited by the Carnot efficiency of a heat engine — they convert mechanical energy directly. This is why hydro remains the largest renewable source worldwide despite decades of solar and wind construction.

Head is easier to buy than flow

Doubling the flow usually means a bigger river, which you cannot arrange. Doubling the head often just means putting the intake further up the hill and running more penstock, which is a cost rather than an impossibility. Small hydro schemes are therefore almost always high-head, low-flow designs.

How much to trust a footprint

Life-cycle figures for the same product routinely differ by a factor of two between studies, because deciding what to count — the farm, the packaging, the shop, the drive home, the disposal — is a methodological choice rather than a measurement. The numbers here are central estimates from published meta-analyses. They are reliable for comparing one option against another, which is what people actually use them for, and not reliable to the second significant figure.

The other thing worth keeping in view is scale. Individual choices matter and they are not where the emissions are: the difference between the best and worst quartile of beef producers is larger than most people's entire dietary footprint, and that is a question about agriculture policy rather than about shopping.