# How To Calculate Carbon Emissions From Flights

As organisations and individuals around the world begin to calculate their carbon footprints, the obvious inclusions are transport, home heating, electricity – and then of course international travel. It’s arguably one of the greatest contributors to greenhouse gas emissions, yet also one of the hardest emitters to accurately calculate.

Various airlines, organisations and platforms such as us here at EnergyElephant have tried to devise methodologies to calculate airline travel emissions in a coherent and efficient manner. EnergyElephant ties airline emissions into its Scope 3 emissions tool in order to help organisations quantify their flights' CO2 outputs. This tool uses the Spherical Law of Cosines to work out the distance between the departure and arrival airport. It then multiplies this figure by a DEFRA emissions factor.

The Spherical Law of Cosines is a theorem relating the sides and angles of spherical triangles. Spherical triangles have been studied since antiquity because of their importance in navigation. The Spherical Law of Cosines is first found in the work of Regiomontanus (1464) and has since been adapted into the theorem used by us today. EnergyElephant uses this theorem on the basis that planes do not fly in direct lines, instead they fly in a curve, relative to the curve in the Earth’s sphere.

Suppose that a spherical triangle on the unit sphere has side lengths a, b and c, and let C denote the angle adjacent to sides a and b. Then (using radian measure):

cos(c) = cos(a) cos(b) + sin(a) sin(b) cos(C).

In order to calculate the air distance from Destination A to destination B, we must know their coordinates. The coordinates are then marked on a globe:

Addis Ababa *(A)*, Boston *(B)*, and the apex which is the North Pole (*P*) are the vertices of a spherical triangle. These are used in the theorem above to calculate the great-circle distance from Addis Ababa to Boston, which gives us a figure in kilometres (km).

This figure is then multiplied by the selected DEFRA (UK Department for Environment, Food and Rural Affairs) emission conversion factors. These conversion factors then give an emission figure for the calculated flight. Whilst this is one methodology, there are many ways that carbon emissions from flights can be calculated, with various organisations opting for different approaches.

The International Civil Aviation Organization (ICAO) has developed its own methodology to calculate the carbon emissions from air travel. They have developed a tool in the form of a Carbon Emissions Calculator, which people can use to calculate carbon emissions attributed to them from their flights. The calculator requires the departing airport, destination airport and class type in order to calculate the individual's flight emissions.

For example: An individual taking a return flight in economy class from Dublin to London Gatwick will be responsible for emitting 123.8 kg** **of carbon on the journey, by the calculator’s estimations. That is a pretty high figure for a fairly short-haul flight.

The ICAO states that they employ "industry averages for the various factors which contribute to the calculation of the emissions associated with the individual passenger’s air travel." These averages are necessary as passengers’ aviation emissions are affected by continuously changing variables specific to each flight. These variables include a variety of factors such as class type, route changes, weather influences, plane capacity and passenger to cargo ratios.

A carbon calculator can only roughly estimate the flight emissions of an individual, due to these constraints. These methodologies are developed in order to achieve the best average possible. Of course a more accurate approach requires much more detailed data. Companies such as OAG provide flight databases and statistics recovered from real time analysis of the air travel ecosystem. These databases are critical in creating steadfast methodologies.

Many major airlines have developed their own carbon calculators to provide passengers with an estimated individual carbon attribution before booking their flight. Aviation currently accounts for 2.4% of all global CO2 emissions. However, other industries are beginning to reduce their dependence on fossil fuels, with renewable sources become increasingly available and more cost effective. As aviation is an industry that cannot yet implement the switch to more renewable sources, it risks accounting for an ever-growing share of global CO2 emissions.

Under CORSIA, the Carbon Offsetting and Reduction Scheme, airlines are now required to report on their carbon emissions. As reporting is now legally obligated, airlines are keen to notify passengers of their individual attribution and encourage them to opt in for carbon offsetting schemes.

Aer Lingus is an example of one major airline that has created its own carbon calculator. Aer Lingus’ calculator like all other carbon calculators is a tool that converts activity data, such as distance travelled or litres of fuel burned into carbon emissions. Their methodology uses conversion factors that are generated by the UK government’s Department for Business, Energy and Industrial Strategy (BEIS). They also state that the data in the calculator is updated regularly based on: changes to flight destinations, new emissions factor data and other changes to emissions regimes.

Furthermore, Aer Lingus’ methodology uses a radiative forcing** **index of 1. Radiative forcing is defined as ‘the change in energy flux in the atmosphere caused by natural or anthropogenic factors of climate change’. It is a scientific concept used to quantify and compare the external drivers of change to the Earth's energy balance, devised by the International Panel on Climate Change (IPCC). Their research indicates that CO2 and other gases have a greater impact when released at altitude, than when they are released on land. However, the relative scale of impact is not definitive, thus it acts as another variable in the calculation of aviation emissions.

Currently there are no internationally agreed and adopted methodologies for the calculation of flight emissions. Until an international standard is devised, it is imperative that organisations are transparent in the methodologies used in the calculation of carbon emissions from flights. Due to the underlying assumptions made in respective carbon calculation methodologies, no two carbon calculators will produce the same result. At EnergyElephant transparency is key, therefore, we are happy to disclose our methodologies for carbon flight emission calculation, as outlined in this article. With informed data, we can all play our part in reducing our environmental impact.

**Sources**

https://www.theoremoftheday.org/GeometryAndTrigonometry/SphericalCos/TotDSphericalCos.pdf

https://www.math.stonybrook.edu/~tony/archive/hon101s08/spher-trig.html

http://www.math.ucdenver.edu/~hartkes/teaching/2011m896/SphericalLawOfCosines.pdf

https://www.oag.com/how-green-is-your-airline

https://www.pureleapfrog.org/aer-lingus/carbon-neutral/

https://www.eci.ox.ac.uk/research/energy/downloads/jardine09-carboninflights.pdf