Breguet Range Equation Calculator

The Breguet range formula predicts how far a jet aircraft can fly in the cruise phase, based on four factors: flight speed, the efficiency with which engines convert fuel into thrust, the aerodynamic performance of the aircraft as it moves through the air and the percentage of the total weight of the aircraft that is fuel. The formula is named after French aircraft manufacturer Louis Charles Breguet.

Enter five of the six values and leave the sixth blank. The calculator will determine the missing value and enter it into the result, allowing you to calculate range, determine fuel required, or back-calculate the lift-to-drag ratio for a given mission requirement. The graph below shows how range reacts to changes in both the fuel ratio and the lift-to-drag ratio.

What is the Breguet range formula?

This formula combines three independent factors that are usually referred to as the "three pillars of reach".

The first term, V divided by the product of g and c, is the thrust term. It indicates how far an aircraft flies per unit of fuel consumed. V is the travel speed, g is the acceleration due to gravity, and c is the specific fuel consumption (fuel consumption per unit of thrust per time).

The second term, L divided by D, is the lift-to-drag ratio and a direct indicator of aerodynamic efficiency. For modern commercial transport aircraft this value typically lies between 15 and 20, while for combat aircraft it usually hovers around 4 to 8.

The third term is the natural logarithm of the weight ratio, i.e. the result of dividing the weight at the start of the flight by the weight at the end of the flight. As fuel is consumed, the aircraft becomes lighter and less thrust is required. Because this term is a logarithm, the effect of the fuel gradually reduces. Doubling the fuel ratio does not double the range.

How to use this calculator:

Enter cruise speed, specific fuel consumption (TSFC), lift to drag ratio and the two cruise weights and leave the range field blank to calculate range. Each field has a separate unit toggle so you can freely mix metric and imperial units. To calculate another value, leave that field blank and enter the range. The main window shows cruise range while the overlay card shows fuel consumption, fuel ratio, weight ratio and flight time.

Example calculation:

Consider a long-haul freighter flying at 250 m/s (roughly 900 km/h). The TSFC is 15 g/(kN·s), the lift-to-drag ratio is 18, the initial weight is 200,000 kg and the final weight is 150,000 kg. During the flight, 50,000 kg of fuel are consumed.

First the weight ratio is calculated: The natural logarithm is taken by dividing 200,000 by 150,000.

First the thrust coefficient is calculated. Velocity, gravity and TSFC (thrust specific fuel consumption) are combined with the TSFC converted to base units of kg/(N·s). So 15 g/(kN·s) equals 0.000015.

Thirdly, the three factors are multiplied together.

This is roughly the distance from New York to Tokyo. Although fuel makes up a quarter of an airplane's weight, the natural logarithm of the ratio remains about 0.288, reducing the end result. This is why designers strive to reduce empty weight by even one kilogram and increase lift-to-drag ratio by one point.

List of variables:

The following symbols are shown as fields in the calculator. The example values are the numbers used in the calculation example above.

Lift to drag ratio for various aircraft types.

The lift-to-drag ratio is a single number that summarizes the aerodynamic efficiency of an aircraft during cruise flight. Typical values are usually in this range:

Assumptions and limitations

The Breguet range formula describes only the cruise flight and assumes that the aircraft is in a steady state of flight, i.e. speed and lift-to-drag ratio are constant, and that specific fuel consumption (TSFC) remains fairly constant over the entire flight envelope. In reality there will be small deviations due to gradual climbs and speed adjustments. Also this formula assumes that fuel is burned to reduce the weight of the aircraft which means it cannot directly apply to battery powered electric aircraft where the weight remains constant during the flight. For conventional jet aircraft, with exact input of cruise conditions, calculated results typically deviate by 5 to 10 percentage points from actual measured values.

Applications of the Breguet formula

Aircraft designers use this formula in early design stages to determine the amount of fuel required for a given mission and to examine various trade-offs; e.g., whether the range increase gained by a more fuel-efficient engine outweighs the benefits of aerodynamic improvements that increase the lift-to-drag ratio. Airlines use it to determine if a particular route can be flown without an in-flight refueling with a given payload. It is also a simple teaching tool showing how decisions on engines, airframe and fuel affect range.

How to get accurate estimates

The values used are for flight conditions, not ground roll or takeoff data. TSFC (Thrust specific fuel consumption) and L/D (lift to drag ratio) vary with altitude and Mach number. The initial weight and final weight are only set for the leg while reserve fuel, rolling fuel, and climb fuel are calculated separately. The weight ratio should be realistic values as the results are affected by its logarithm. Also note that the values given here are estimates for planning purposes only and do not replace a full mission analysis.