Compute how far a jet aircraft can fly on a single tank of fuel using the Breguet range equation. Adjust the cruise speed, lift-to-drag ratio, engine fuel economy and fuel fraction to see the range, endurance and weight ratio update in real time, and learn how three efficiencies — aerodynamic, engine and weight — together set the range.
Parameters
Cruise speed V
m/s
True airspeed during cruise
Lift-to-drag ratio L/D
Aerodynamic efficiency. Higher means more lift per unit drag
Thrust-specific fuel consumption c
1/h
Engine-efficiency metric. Lower means better fuel economy
Fuel fraction (fuel / take-off weight)
Share of the take-off weight that is fuel
Results
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Weight ratio W0/W1
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Log term ln(W0/W1)
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Range (km)
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Endurance (h)
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Converted fuel rate (1/s)
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Range class
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Cruise & fuel burn — flight animation
The aircraft cruises along a ground track and the fuel tank drains as it flies. The bars below show the magnitude of the three factors that set the range: lift-to-drag ratio, fuel consumption and weight ratio.
The jet form of the Breguet range equation, R [m]. Range is the product of aerodynamic efficiency (lift-to-drag ratio L/D), engine efficiency (1/c) and the logarithm of the weight ratio ln(W0/W1).
The weight ratio is the take-off weight W0 divided by the landing weight W1, obtained from the fuel fraction W_f/W0. The endurance t_E [s] is the range divided by the cruise speed.
$$c_{\text{SI}}=\frac{c}{3600}$$
The thrust-specific fuel consumption converted from per-hour [1/h] to per-second [1/s]. The term V/c is evaluated in SI units.
What is the Breguet Range Equation?
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I have never heard of the "Breguet range equation". Is it the equation for how far an aircraft can fly?
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Exactly that. It was derived by the French aviation pioneer Breguet in the early days of flight, and it gives a beautifully compact answer to how far a jet aircraft can fly on a full tank. It has the form R = (V/c)·(L/D)·ln(W0/W1), and the elegant part is that range comes out as the product of three "efficiencies". The designer can attack each of those three independently.
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Three efficiencies… what exactly are they?
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The first is aerodynamic efficiency — the lift-to-drag ratio L/D. A high L/D means the wings make the necessary lift with little drag, so you need less thrust and less fuel. That is why long-range aircraft have long, slender, high-aspect-ratio wings. The second is propulsive efficiency, captured by the engine's specific fuel consumption. A modern high-bypass turbofan sips far less fuel than an old turbojet. The third is structural-and-fuel efficiency, and that is the weight ratio.
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The weight ratio is what changes when I move the "fuel fraction" slider on the left, right? But surely the more fuel you load, the farther you can fly?
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Good catch — that is where the "logarithm" in the equation kicks in. Range is proportional to the logarithm of the weight ratio, ln(W0/W1). A logarithm grows more and more slowly as its input increases, so loading more and more fuel gives diminishing returns. And the extra fuel itself has to be carried. Look at the "Range vs fuel fraction" chart below and you will see the curve gradually flatten out.
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I see… so to double the range you would have to load far more than double the fuel.
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Precisely. This is what people call the "cruel arithmetic" of long-range flight. Because of that logarithm, doubling the range requires a fuel fraction far larger than twice the original. That is why ultra-long-range aircraft are so hard to design. The "Range vs L/D" chart, on the other hand, is a straight line through the origin — double the L/D and the range simply doubles. In many cases polishing the aerodynamics beats just adding fuel.
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Is this equation actually used when real aircraft are designed?
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It is the very foundation of aircraft conceptual design and mission planning. When engineers first size the wing, engine and fuel capacity to fly, say, Tokyo to New York, the Breguet equation is what they use. It also governs the "endurance" of long-loiter drones and reconnaissance aircraft. Just remember that this jet form assumes a steady cruise at constant lift coefficient and constant speed, so it does not include the fuel used in take-off or climb. The real range is a bit smaller than this estimate.
Frequently Asked Questions
The Breguet range equation gives how far a jet aircraft can fly on the fuel it carries. The jet form is R = (V/c)·(L/D)·ln(W0/W1), where V is the cruise speed, c is the thrust-specific fuel consumption, L/D is the lift-to-drag ratio and W0/W1 is the ratio of take-off weight to landing weight. It shows that range is the product of three efficiencies — aerodynamic efficiency (L/D), engine efficiency (1/c) and the logarithm of the weight ratio — and a designer can attack each one independently.
Range is proportional to the logarithm of the weight ratio, ln(W0/W1). Adding fuel raises the weight ratio, but the logarithm grows more and more slowly as its input increases. On top of that, the extra fuel must itself be carried and lifted, which costs fuel. As a result, increasing the fuel fraction gives diminishing returns, and doubling the range requires far more than doubling the fuel fraction. This is the cruel arithmetic of long-range flight.
In the Breguet equation, range is directly proportional to L/D. A high L/D means the wings produce the necessary lift while creating little drag, so little thrust and little fuel are needed. The range-versus-L/D curve is a straight line through the origin: double the L/D and you double the range. Long-range aircraft have long, slender, high-aspect-ratio wings precisely because raising L/D raises range so directly.
This jet form of the Breguet equation assumes a steady cruise at constant lift coefficient — that is, a constant cruise speed with the lift-to-drag ratio L/D and specific fuel consumption c roughly constant throughout the flight. It does not include the fuel burned during take-off, climb and descent, head or tail winds, or reserve fuel. The real operational range is normally smaller than this estimate, so treat the tool's result as the ideal cruise-segment range.
Real-World Applications
Airliner conceptual design: When a new airliner is conceived, designers work backwards from the routes they want to serve — that is, the required range — using the Breguet equation. The starting point for deciding how high to push the lift-to-drag ratio, which engine to choose and how large to make the fuel tanks is exactly this equation. Long-range aircraft like the 787 and A350 use composite, slender wings and high-bypass engines because that attacks all three terms of the Breguet equation at once.
Operations and mission planning: Even for in-service aircraft, the Breguet equation underlies the trade-off between payload (passengers and cargo) and fuel load. More fuel lets the aircraft fly farther, but the payload must be cut accordingly. Because of the logarithmic weight-ratio effect, the longest routes severely limit how many passengers can be carried. The payload-range diagram has the Breguet equation as its backbone.
Long-endurance aircraft and drones: For reconnaissance aircraft and solar or electric long-loiter drones, "endurance" matters more than range. Endurance equals range divided by speed, and flying slowly while holding a high lift-to-drag ratio keeps the aircraft aloft longer. Aircraft like the Global Hawk have extremely slender wings precisely to maximise the L/D that governs loiter time.
Evaluating fuel-economy and decarbonisation gains: The Breguet equation is handy for quickly estimating how much a new wingtip device (winglet), a laminar-flow wing, lighter composites or a next-generation engine will improve range and fuel economy. A few percent rise in L/D, a few percent drop in c, a lighter structure — you can move the sliders in this tool and see how each one feeds into the range.
Common Misconceptions and Pitfalls
The biggest misconception is treating the range from the Breguet equation as the real operational range of the aircraft. This jet form covers only an idealised steady cruise at constant lift coefficient and constant speed. A real flight includes take-off, climb and descent, which burn a significant amount of fuel. You also need reserve fuel in case you cannot land, fuel to an alternate airport and a margin for headwinds. After subtracting all of that, the operational range comes out smaller than the value this tool shows. Treat the result as the "ideal cruise-segment value" and a "sensitivity indicator" for the design.
Next, getting the units of the specific fuel consumption c wrong. The jet Breguet equation uses the thrust-specific fuel consumption — the weight of fuel burned per hour per newton of thrust — and you must convert it to a per-second value before evaluating V/c. This tool divides the input c [1/h] by 3600 to get [1/s]. Propeller aircraft use a completely different form (with the power-specific fuel consumption and the propeller efficiency), and the range there does not even depend on speed in the same way. Do not mix up the jet form and the propeller form.
Finally, the belief that "loading more fuel lets you fly indefinitely farther". Range is proportional to the logarithm of the weight ratio, so the gain becomes ever smaller as the fuel fraction grows. The loaded fuel also makes the aircraft heavier, demands a stronger structure and runs into the maximum take-off weight limit. Beyond a certain point, polishing the lift-to-drag ratio or switching to a more efficient engine is far more effective than adding fuel. The Breguet equation is also a tool for quantitatively deciding where to invest.
How to Use
Enter initial aircraft weight W0 (kg) and final weight W1 (kg) after fuel burn to calculate weight ratio
Input cruise velocity (m/s), thrust-specific fuel consumption TSFC (kg/N·h), and gravitational constant g (9.81 m/s²)
The simulator computes Breguet range using R = (V/g)·(L/D)·TSFC⁻¹·ln(W0/W1) where L/D is lift-to-drag ratio
Review output statistics: weight ratio, logarithmic term, range in km, endurance in hours, and fuel flow rate in kg/s
Worked Example
Boeing 747-400 cruising at 490 m/s with TSFC = 0.0155 kg/N·h, L/D = 17.2, W0 = 412,775 kg, W1 = 178,756 kg (landing weight). Weight ratio = 2.31, ln(2.31) = 0.837. Range = (490/9.81)·17.2·(1/0.0155)·0.837 = 7,422 km. Endurance ≈ 15.1 hours. Fuel consumed = 234,019 kg.
Practical Notes
TSFC varies with altitude and engine throttle: turbofans at cruise (35,000 ft) typically 0.012–0.018 kg/N·h; adjust for step-climbs as fuel burns and aircraft weight reduces
L/D estimation critical—use actual flight test data or CFD results; wide-body jets range 16–18, regional turboprops 20–25
Reserve fuel (5–10% of initial weight) reduces available fuel weight; account in W1 calculation for regulatory compliance
Simulator assumes constant cruise conditions; real operations include climb, descent, taxi consuming 8–15% additional fuel