Which element is the cheapest to bend?

Air. Energy scales with density times velocity squared, and air is about 800× less dense than water, so a wind blast costs far less than an equivalent water blast. Fire is the most expensive because heating mass via mcΔT with water's specific heat of 4184 J/kg·K demands hundreds of kilojoules.

Avatar · bending energy budget

Every bend has a thermodynamic price.

Pick an element. Set how much mass you move and how fast — or how hot. The energy cost recomputes through the right physics. Air is nearly free; Fire is a small power station.

Energy required— J

—

Same move, all four elements — cheapest to most expensive

Set the bend

Mass / amount10 kg

Velocity10 m/s

What that energy equals

—

Worked examples

How to read it

Pick an element, then drag mass and the second slider — velocity for Water and Air, height for Earth, temperature rise for Fire. The big number is the energy that bend costs, and the ranking bars show the same move priced across all four elements at once.

The formula switches with the element: Water and Air spend kinetic energy ½mv², Earth pays gravity mgh, Fire pays heat mcΔT.

Why Air is the cheapest

Air pressure changes propagate via molecular collisions — you barely need to move air to redirect it. Energy ∝ density × velocity². Air is 800× less dense than water, so a wind-blast costs 800× less than a water-blast of the same kinetic energy.

Why Fire is the most expensive

Combustion creates heat from chemical bonds. To generate fire without fuel (like Azula's lightning), you need to deliver kilojoules per second sustained — equivalent to running a hair dryer.

Or in lightning terms: 10⁹ V × 30 kA × 30 μs = ~900 kJ per bolt. Azula throws a small power station.

Earthbending: gravity is most of the price

Lifting 100kg of rock 2m: E = mgh = 1,962 J. About 470 calories. A solid push-up's worth.

Hurling that rock at 30 m/s adds ½mv² = 45,000 J — 22× more. The acceleration costs, not the lift.

Citations

Halliday, Resnick & Walker (2014) — Fundamentals of Physics. KE = ½mv², PE = mgh, Q = mcΔT.
NIST Webbook — specific heat of water 4184 J/(kg·K), air density 1.225 kg/m³ STP.
Uman (2001) — The Lightning Discharge. Bolt energy ~10⁸–10⁹ J.
Rasmussen (1971) — basal-metabolic energy budget ~100 W sustained.
Kakalios (2009) — The Physics of Superheroes, ch. on elemental bending energy accounting.

Built by Joshua Chua · Fable rebuild · vanilla JS + Canvas