Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Hot Air Balloons - Calculate Lifting Weights

Calculate hot air ballons lifting forces.

Air Balloon - Hot Air Lifting Force

Hot Air Lifting Force

The lifting force from a hot air balloon depends on the density difference between balloon air and surrounding air, and the balloon volume. The lifting force can be calculated as

F l = V (ρ c - ρ h ) a g (1)


F l = lifting force (N, lbf )

V = balloon volume (m3, ft3 )

ρ c = density cold surrounding air (kg/m3, slugs /ft3 )

ρ h = density hot balloon air (kg/m3, slugs /ft3 )

a g = acceleration of gravity (9.81 m/s2, 32.174 ft/s2)

Example - Lifting Force created by a Hot Air Balloon

A hot air balloon with volume 10 m3 (353 ft3 ) is heated to 100 oC (212 oF) .   The temperature of the surrounding air is 20 oC (68 oF). The air density at temperature 100 oC is 0.946 kg/m3 (0.00184 slugs/ft3 ) and the air density at temperature 20 oC is 1.205 kg/m3 (0.00234 slugs/ft3 ) .

The lifting force can be calculated as

F l = (10 m3 ) [(1.205 kg/m3 ) - (0.946 kg/m3 )] (9.81 m/s2)

= 25.4 N

Weight - or gravity force - can be calculated as

F g = m a g (2)


F g = weight - gravity force (N, lbf )

m = mass (kg, slugs )

Since lifting force of a flying air balloon equals weight (F l = F g ) - the lifted mass can be expressed by combining (1) and (2) to

m = F l / a g

= (25.4 N) / (9.81 m/s2)

= 2.6 kg

The calculation of lifting force can be done in Imperial units as

F l = (353 ft3 ) [(0.00234 slugs/ft3 ) - (0.00184 slugs/ft3 )] (32.174 ft/s2)

= 5.7 lbf

Hot Air Balloon - Specific Lifting Force

Specific lifting force (force per unit air volume) created by an hot air balloon - balloon temperature vs. surrounded air temperature - are indicated in the charts below.

SI - units

Hot Air Balloon - Specific Lifting Force

Imperial Units

Hot Air Balloon - Specific Lifting Force - Imparial Units

Example - Specific Lifting Force from a Hot Air Balloon

Hot Air Balloon - Lifting Force Example

If the balloon temperature is 60 oC and the surrounded temperature is -20 oC - the chart indicates a specific lifting force

3.3 N/m3

Hot Air Balloon Lifting Force Calculator

This calculator can be used to calculate the lifting force of a volume with lower density than surrounding air.

Related Topics

  • Mechanics

    The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

Related Documents

  • Air - Thermophysical Properties

    Thermal properties of air at different temperatures - density, viscosity, critical temperature and pressure, triple point, enthalpi and entropi, thermal conductivity and diffusivity and more.
  • Buoyancy

    Buoyancy is the resultant force acting on a submerged body.
  • Elevators - Force and Power

    Required force and power to lift an elevator.
  • Force

    Newton's third law - force vs. mass and acceleration.
  • Lift and Drag

    Lift and drag forces acting on a body like an air foil in a fluid flow.
  • Mass vs. Weight

    Mass vs. weight - the Gravity Force.


Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

We use a third-party to provide monetization technologies for our site. You can review their privacy and cookie policy here.

You can change your privacy settings by clicking the following button: .


This page can be cited as

  • The Engineering ToolBox (2003). Hot Air Balloons - Calculate Lifting Weights. [online] Available at: [Accessed Day Month Year].

Modify the access date according your visit.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter