Power Required at Altitude Calculator

Air density

True airspeed

Reference area

Drag coefficient

Power required

Find air density from altitude

Enter an altitude and read off the ISA standard air density to use above.

Compare power at another altitude

Project the true airspeed and power needed for level flight at a target altitude.

Power required

Drag force: kN
Air density vs sea level: %

Power grows with the cube of speed. Fly twice as fast and you need about eight times the power, so a modest speed increase is expensive.

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Show power vs true airspeed

Plot how required power climbs with the cube of speed.

Show power vs altitude

Plot required power at standard altitudes for the same true airspeed.

Show the standard atmosphere table

Air density and required power from sea level to 12 km.

Required power at standard altitudes for your true airspeed, area, and drag coefficient
Altitude	Air density (kg/m³)	Density vs sea level	Power required (kW)
Sea level	1.225	100.0%	306.25
1,000 m	1.112	90.8%	277.92
2,000 m	1.007	82.2%	251.65
3,000 m	0.909	74.2%	227.33
4,000 m	0.819	66.9%	204.85
5,000 m	0.736	60.1%	184.1
6,000 m	0.66	53.9%	165.03
8,000 m	0.526	42.9%	131.45
10,000 m	0.413	33.8%	103.37
11,000 m	0.365	29.8%	91.2
12,000 m	0.312	25.5%	77.97

As altitude increases the air becomes thinner and the power required to maintain flight also changes. This calculator uses an aerodynamic power formula to calculate the power required for constant horizontal flight based on air density, true airspeed, wing area, and drag coefficient. Enter any four of these values and the remaining value will be calculated so you can see the result without having to manually rearrange the formula.

What performance is required at high altitude?

The power required is the amount of energy an aircraft must produce per second to overcome drag and maintain level flight. The basic concept is that power equals force times velocity. During flight, this force corresponds to the drag which is determined by air density, true airspeed, wing area, and the drag coefficient. Combining these factors allows us to determine the required power.

Altitude affects performance through air density. At 10,000 m the air is about a third as dense as at sea level. If true airspeed remains constant this means less drag and therefore lower power required. There is another effect though; to carry the same weight in thinner air the aircraft must fly faster. Since power varies with the cube of speed this increase in speed leads to an additional increase in power required. Which of these effects dominates depends on the type of flight, and it is the task of this tool to show that.

How to use the calculator:

Enter the air density, true airspeed, reference area and drag coefficient to find the power required. Conversely you can leave one of these values blank and enter the other four to find the value that you are looking for. From a known power you can calculate the speed that will be maintained by this power or the drag coefficient corresponding to the measured power. The altitude correction option allows you to convert an altitude into standard air density. The climb comparison option allows you to determine the true airspeed and power required to climb to a given target altitude at level flight.

Output formula.

The air resistance $F_D$ is calculated from the formula for drag force and power is the product of this force and speed.

F_D = \tfrac{1}{2}\,\rho\,v^{2}\,S\,C_D \qquad P = F_D\,v = \tfrac{1}{2}\,\rho\,v^{3}\,S\,C_D

Consider, for example, a light aircraft with $S = 20\ \text{m}^2$ and $C_D = 0.025$ flying at a speed of 100 m/s at sea level.

P = \tfrac{1}{2}(1.225)(100)^{3}(20)(0.025) = 306{,}250\ \text{W} \approx 306\ \text{kW}

Now consider the case where this plane is flying at an altitude of 10,000 meters. In that case, the air density will be about 0.413 kg/m3.

P = \tfrac{1}{2}(0.413)(100)^{3}(20)(0.025) \approx 103\ \text{kW}

At the same relative airspeed, the power required is reduced to about one-third of that at sea level. This reduction in aerodynamic drag is the main reason why commercial airliners fly at high altitudes. The following table shows all symbols used and their corresponding values for this example.

Symbol	Meaning	Example
$P$	Power required	306 kW at sea level
$\rho$	Air density	1.225 $kg/m^3$
$v$	True airspeed	100 m/s
$S$	Reference area	20 $m^2$
$C_D$	Drag coefficient	0.025

Rearranging an equation to find any value.

This equation is simple to transform as it only represents the product of several quantities. This calculator will select the appropriate form based on the values entered. To calculate velocity, a cube root is used.

C_D = \frac{2P}{\rho\,v^{3}\,S} \qquad v = \sqrt[3]{\frac{2P}{\rho\,S\,C_D}}

The first equation can be used to convert the measured power into a corresponding resistance coefficient. The second equation shows how fast an aircraft can fly with given power.

Why altitude has a double effect:

The question "how does power change with altitude" has two valid answers depending on what is held constant. If true airspeed is held constant, then power required is proportional to air density so that going up will save power. If weight in level flight is held constant, it's exactly the opposite. The wings must generate the same amount of lift, so at lower densities the plane has to go faster which results in a power requirement that actually increases with altitude. This increasing power requirement is why every airplane has a maximum operating altitude - the altitude where the power required to maintain level flight in thin air equals the power remaining available from the engines.

v_2 = v_1\sqrt{\frac{\rho_1}{\rho_2}} \qquad P_2 = P_1\sqrt{\frac{\rho_1}{\rho_2}}

The Climb Compare option uses these relationships at level flight. It calculates the standard air density for the target altitude based on current conditions and shows a higher true airspeed and power required to hold the same weight at that altitude.

Standard air tightness.

The air density decreases predictably with altitude. The numerical values of the international standard atmosphere that should be entered in the "air density" field also serve to activate the integrated altitude charts and data tables.

Altitude	Air density	Fraction of sea level
Sea level	1.225 $kg/m^3$	100%
2,000 m	1.007 $kg/m^3$	82%
5,000 m	0.736 $kg/m^3$	60%
8,000 m	0.526 $kg/m^3$	43%
10,000 m	0.414 $kg/m^3$	34%
11,000 m	0.365 $kg/m^3$	30%

Selection of resistance value:

The drag coefficient is a dimensionless quantity that describes the aerodynamic drag characteristics of an aircraft. It varies with angle of attack, Mach number and configuration of the aircraft so it must be adjusted to match the simulated flight condition. Deploying flaps and landing gear will increase the drag coefficient significantly. Typical values for a clean configuration are given below as a starting point.

Configuration	Approximate Cd
Fighter jet, clean	0.015 to 0.025
Airliner, cruise	0.02 to 0.03
Light aircraft, retractable gear	0.025 to 0.035
Light aircraft, fixed gear	0.04 to 0.05

Scope of this calculation:

The choice of engine is ultimately aimed at matching the available power to the required power over the entire flight profile. This formula gives the required power. Flight planners choose cruise altitude taking into account both the fall in drag at high altitudes and the reduction in engine performance in thin air. The top speed, practical maximum altitude and rate of climb are all dependent on the difference between the required and available power. Thus they are used for both performance analysis and basic training in aircraft energy management.

Tips for more accurate estimates:

Please determine the air density from the standard atmosphere table for your target altitude. Even small errors here can directly affect the result. Use the true velocity vector, not the one indicated by the cockpit relative to the air. These two values diverge gradually as you climb. Remember that this is required power and not actual available power. The engine's own performance also decreases in thinner air so the actual maximum altitude will be at the intersection of the two curves. If approaching or exceeding the speed of sound, wave drag must be included in the drag coefficient otherwise results are too low.

Frequently asked questions

What is the typical drag coefficient for an airplane?

For modern aerodynamically optimized aircraft the drag coefficient is in the range of about 0.015 to 0.05. For fighter jets it's around 0.015 to 0.025, for commercial airliners in cruise flight it's about 0.02 to 0.03, and for light aircraft with fixed undercarriage it can be up to 0.04 to 0.05. When flaps and undercarriage are deployed this value increases.

Why does it take less power at higher altitudes for a given true airspeed?

The power required is the product of half the air density, the cube of the speed, the wing area and the drag coefficient. At a constant true airspeed, the only factor that changes with altitude is the decreasing air density. As lower air pressure results in less drag, so also does it take less power to maintain this speed.

Why do airplanes consume power even when climbing?

In level flight the wing must generate enough lift to support the weight. As density decreases, the plane must fly faster to create this lift and the power required is proportional to the cube of the speed. At constant mass, the power required actually increases with altitude. The maximum operating altitude is where the power required equals the power that can still be produced by the engine in the thin air.

What is the difference between true and indicated airspeed?

True airspeed is the actual speed at which the airplane moves relative to the air. Indicated airspeed is what the pitot-static tube measures, and since the dynamic pressure difference is less at high altitude due to thinner air, indicated airspeed will be lower. Always use true airspeed when calculating power required.

Can this calculator be used for supersonic flight?

The formula itself remains valid but the drag coefficient must include wave drag which rises steeply once Mach 1 is exceeded. Using a subcritical drag coefficient at supersonic speeds will result in values that are much lower than actual.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

NASA Glenn Research Center: The Drag Equation
NASA explainer on the drag equation and each of its terms.
Wikipedia: International Standard Atmosphere
The standard atmosphere model behind the altitude density values.
Wikipedia: Drag equation
Definition of drag force, drag coefficient, and reference area.