Hot air balloons rise because heated air is less dense than the cooler air outside the envelope. The difference in density creates buoyant force, which must exceed the combined weight of the balloon, passengers, and gear. Balloon pilots adjust the temperature inside the envelope to control altitude. This calculator uses a simplified physics model to estimate the volume of hot air required to lift a given payload.
Air density can be approximated with the ideal gas law. Assuming constant pressure, density is inversely proportional to absolute temperature. The buoyant force equals the weight of the displaced outside air minus the weight of the heated air inside. The net lift per cubic meter is:
where is pressure (assume 101,325 Pa), is the specific gas constant for air (287 J/kg·K), and and are the outside and inside temperatures in Kelvin. Multiplying by volume gives total lift.
To lift a payload, the net lift force must equal its weight. Rearranging the equation yields a volume estimate. This tool assumes the balloon envelope itself weighs very little relative to the payload. Real-world balloons add fabric weight, basket weight, and fuel consumption, so you'll need a safety margin in practice.
Enter the payload mass and the temperatures inside and outside the balloon. Warmer internal air creates more lift, but there are limits: extremely hot air can damage the fabric. Typical flights heat air to around 100 °C. Higher outside temperatures or elevations reduce lift because the surrounding air is less dense. Use the output as a starting estimate and consult experienced pilots for precise calculations.
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