Breguet Range Equation Calculator

The Breguet Range Equation predicts how far a jet aircraft can fly during cruise, based on its speed, engine efficiency, aerodynamic performance, and fuel load. It is named after French engineer Louis Charles Breguet. The equation pulls together the three things designers care most about: how efficiently the engines turn fuel into thrust, how cleanly the airframe moves through the air, and how much of the aircraft's weight is fuel. Enter any five of the six variables below to solve for the sixth. The charts further down plot how range responds as you vary the fuel fraction and the lift-to-drag ratio.

What is the Breguet range equation?

The Breguet Range Equation estimates the cruise range of a jet-powered aircraft by combining three independent factors, often called the "three pillars" of range:

R = \frac{V}{g \cdot TSFC} \cdot \frac{L}{D} \cdot \ln\left(\frac{W_i}{W_f}\right)

The first factor, $\frac{V}{g \cdot TSFC}$ , captures propulsion efficiency, or how far the aircraft travels per unit of fuel burned. TSFC (Thrust Specific Fuel Consumption) measures fuel burn rate per unit of thrust. The second factor, $L/D$ , is the lift-to-drag ratio, a measure of aerodynamic cleanliness. Modern commercial jets achieve L/D ratios of 15 to 20, while military fighters sit closer to 4 to 8. The third factor, $\ln(W_i / W_f)$ , is the natural logarithm of the weight ratio. As fuel burns, the aircraft gets lighter and needs less thrust. Because the term is a logarithm, extra fuel gives diminishing returns, so doubling your fuel fraction does not double your range.

How to use this calculator

Enter the cruise velocity of the aircraft. For commercial jets, this is typically 800 to 950 km/h.
Input the TSFC for your engine. Modern turbofans range from 12 to 18 g/(kN·s), or 0.4 to 0.6 lb/(lbf·h).
Set the lift-to-drag ratio. Transport aircraft typically achieve 15 to 20.
Enter the initial weight at cruise start (including remaining fuel) and the final weight at cruise end.
Leave one field blank and it fills in from the other five. To size the fuel load, enter the range and leave a weight field empty.

Each field has its own unit toggle, so you can work in metric or imperial.

Understanding the formula

Take a long-haul cargo jet cruising at 250 m/s (900 km/h), with a TSFC of 15 g/(kN·s), an L/D ratio of 18, an initial weight of 200,000 kg, and a final weight of 150,000 kg. That means it burns 50,000 kg of fuel during cruise.

Step 1: Weight ratio - Calculate the natural log of the weight fraction:

\ln\left(\frac{200{,}000}{150{,}000}\right) = \ln(1.333) \approx 0.2877

Step 2: Propulsion factor - Combine speed, gravity, and TSFC:

\frac{V}{g \cdot TSFC} = \frac{250}{9.807 \times 1.5 \times 10^{-5}} \approx 1{,}699{,}541 \text{ m}

Step 3: Final result - Multiply all three factors:

R = 1{,}699{,}541 \times 18 \times 0.2877 \approx 8{,}799{,}000 \text{ m} \approx 8{,}799 \text{ km}

That is roughly the distance from New York to Tokyo. Even though a quarter of the aircraft's weight is fuel, the logarithmic weight ratio (0.288) tempers the result significantly. This illustrates why aircraft designers obsess over every kilogram of empty weight and every fraction of L/D improvement.

Real-world applications

Size a new aircraft early in design by working out how much fuel a target mission range demands.
Weigh design trade-offs, like whether a lower-TSFC engine buys more range than an aerodynamic tweak that improves L/D.
Check whether a given aircraft can fly a nonstop route at a given payload.
Trace how decades of engine and aerodynamic gains have stretched aircraft range.

Tips for accurate calculations

TSFC varies with altitude and Mach number. Use cruise-condition values, not sea-level or takeoff data.
L/D depends on angle of attack and aircraft configuration. Use the cruise L/D, not the maximum L/D.
Initial and final weights should reflect the cruise segment only. Reserve fuel, taxi fuel, and climb fuel are separate.
The equation assumes constant speed and altitude throughout cruise. Real flights involve stepped climbs and speed adjustments that introduce minor deviations.

Frequently asked questions

Does this equation account for takeoff and landing?

No, it covers the cruise phase only. Total mission fuel also includes reserves, taxi, climb, descent, and diversion allowances, so budget those separately.

Can I use this for propeller aircraft?

A different form of the equation applies to propeller-driven aircraft. It replaces V/TSFC with propeller efficiency divided by power-specific fuel consumption.

Why doesn't doubling the fuel double the range?

The natural logarithm creates diminishing returns. Extra fuel adds weight, which increases drag, which burns more fuel. That feedback loop is why squeezing out more range is so hard.

What L/D ratio should I use?

For commercial transports: 15 to 20. Regional jets: 12 to 16. Business jets: 10 to 14. Fighter aircraft: 4 to 8. Use values published for the specific airframe at cruise conditions.

How accurate is this equation?

The Breguet equation typically predicts cruise range within 5 to 10 percent of actual performance for conventional jet aircraft, assuming accurate input values at the correct flight conditions.