✈️ Calculators

Breguet Range (Jet Aircraft)

Calculates a jet aircraft's cruise range with the Breguet equation: speed divided by thrust specific fuel consumption, times the aerodynamic efficiency, times the natural logarithm of the ratio between weight at the start and at the end of cruise. Valid for cruise with V, specific fuel consumption and L/D held constant — in practice the cruise-climb, at fixed Mach and lift coefficient, or step-climb flight. Enter the speed, TSFC, L/D and both weights.

Cruise speed V (km/h) Thrust specific fuel consumption TSFC (h⁻¹) Aerodynamic efficiency L/D Weight at cruise start Wi (kgf) Weight at cruise end Wf (kgf)

Result

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The equation that turns fuel fraction into kilometres

The question turns up early in conceptual design: with this wing, this engine and this fuel fraction, does the aircraft meet the range requirement? The Breguet equation is the fast answer, and it is also the exercise that shows up in every flight performance course. Sizing a tank means checking whether maximum take-off weight still closes; studying for the exam means fighting imperial units in half the textbooks while the clock runs. Without the figure, sizing degenerates into trial and error around MTOW.

R = (V / c) × (L/D) × ln(Wi / Wf). V is true cruise speed in km/h, c is thrust specific fuel consumption in kilograms of fuel per kilogram-force of thrust per hour, numerically an inverse hour, L/D is aerodynamic efficiency, and Wi and Wf are the weights at cruise start and cruise end. Units close on their own: km/h over h⁻¹ leaves km. Each factor speaks for one part of the aircraft — V/c measures the engine, L/D measures the airframe, and the logarithm measures how much fuel went aboard. A modern high bypass turbofan runs c between 0.55 and 0.65; a transport jet cruises with L/D from 15 to 19. The screen values of 850 km/h, 0.6, 17, 72,000 and 58,000 kgf return 5207.4 km.

The derivation demands constant V, c and L/D throughout the cruise. That describes a cruise climb or a stepped flight profile, where the aircraft drifts up as fuel burns off and holds the lift coefficient at the best L/D point. At rigidly fixed altitude with fixed Mach, L/D slips away from the optimum and the result turns slightly optimistic. The range computed here covers cruise alone: take-off, climb, descent, holding, reserves and wind all sit outside it. Propeller aircraft need a different form, built around propeller efficiency and specific power consumption. If Wi comes in below Wf, or any entry arrives at zero or negative, the page shows the warning.

Frequently asked questions

Why is the answer larger than the published range?

Because the equation covers cruise alone. A published range already sets aside fuel for start, take-off, climb and descent, plus the regulatory reserve: thirty to forty-five minutes of holding and a diversion to an alternate airport. Wind piles on top, and a leg with a headwind component can cost hundreds of kilometres. The screen values give 5207.4 km of pure cruise, while the matching book mission would be far shorter. To land nearer reality, enter a Wf that still carries the reserve fuel on board.

Can I enter TSFC in pounds per pound-force per hour?

Yes, with no conversion at all. Thrust specific fuel consumption in pounds of fuel per pound-force of thrust per hour is numerically identical to the value in kilograms per kilogram-force per hour, since the mass and force units cancel in the same ratio and what survives in both cases is an inverse hour. The one form that cannot go in raw is the SI figure in kilograms per newton per second: multiply that by 35,304 first. A modern turbofan sits near 1.7 × 10⁻⁵ in SI units, which lands on 0.60 here.

When does the calculator show the error message?

Whenever an entry makes the arithmetic impossible: speed, specific fuel consumption, aerodynamic efficiency or final weight at zero or below, or a start weight smaller than the end weight. That last case comes up most often and is nearly always a swapped field, since weight at the start of cruise has to be the larger of the two — an aircraft only sheds mass by burning fuel. Empty boxes get different treatment and raise no warning; the readout simply falls back to a dash until all five values are filled in.

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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.