Calculate how fast an aircraft can gain altitude using the excess-power method. Adjust the weight, available engine power, power required for level flight and climb airspeed to see the rate of climb, climb angle and climb gradient update in real time, and build an intuition for how aircraft gain height.
Parameters
Aircraft weight W
N
Weight of the aircraft in flight (gravity x mass)
Available power (propulsive) P_av
kW
Power the engine can deliver at this altitude and throttle
Power required for level flight P_req
kW
Power needed to overcome drag and stay in level flight
Climb airspeed V
m/s
Airspeed along the flight path during the climb
Results
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Excess power (kW)
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Rate of climb (m/s)
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Rate of climb (m/min)
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Climb angle (deg)
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Climb gradient (%)
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Climb performance
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Climbing flight — excess power and velocity vectors
The aircraft climbs along a flight path inclined at the climb angle. The velocity vector splits into a vertical component (rate of climb) and a horizontal component, and the side bar shows available, required and excess power.
The rate of climb RC is the excess power (available power minus required power) divided by the weight W, and the climb angle gamma follows from sin(gamma) = RC/V with airspeed V. At the absolute ceiling, where the excess power reaches zero, the rate of climb also falls to zero.
Horizontal ground speed V_horiz and climb gradient. The gradient is the height gained per unit horizontal distance and forms the basis of obstacle-clearance limits around airports.
What is rate of climb and excess power?
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An aircraft is a lump of metal weighing many tonnes. Where does the energy to lift it higher and higher actually come from?
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Great question. The answer comes down to a single idea: excess power. Think of the engine's job in two parts. To simply keep flying straight and level, the aircraft needs a certain amount of power just to overcome drag - call this the power required. The engine, at a given throttle setting and altitude, can deliver a certain power - the power available. The difference between the two is the excess power.
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I see, it's the difference. But why does that "left-over power" turn into altitude?
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The excess power is power that is not being spent fighting drag. So it has nowhere to go but into raising the aircraft's gravitational potential energy. Divide the excess power by the aircraft's weight and you get, directly, how many metres of height it can gain each second. That is the rate of climb. Try moving the "available power" slider on the left toward the required power - watch the excess shrink and the rate of climb fade away.
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You're right - when I lower the available power the rate of climb hits zero. Does this really happen to actual aircraft?
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It does. The higher you go, the thinner the air, and the less power the engine can deliver. The power required changes more slowly, so the excess keeps shrinking. At a certain altitude the excess power reaches zero - that is the absolute ceiling, and the aircraft can climb no higher. The same reasoning explains why a fully loaded aircraft, or one on a hot day, climbs sluggishly: thinner or "heavier" conditions cut the excess power.
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The results show "climb angle" and "rate of climb" separately. Are these two different things?
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Yes, they are different. The rate of climb is "how many metres you gain per second"; the climb angle is "how steeply the flight path tilts away from the horizontal". They are linked by sin(gamma) = RC/V, so for the same rate of climb a slower speed gives a steeper angle. Whether you clear a building or a hill right after take-off depends on the climb angle, not the rate. And the climb angle is set by excess thrust, not excess power. Confuse the two and you will badly mis-estimate take-off performance.
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I see. So when a fighter jet is described as highly manoeuvrable, is that related to excess power too?
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Very much so. In the fighter world, "specific excess power" - the excess power divided by weight - is the master measure of energy manoeuvrability. An aircraft with high specific excess power can climb fast, accelerate fast and gain a better position than an opponent. So the rate of climb that this tool deals with is a fundamental quantity that governs not just airline operations but the outcome of air combat.
Frequently Asked Questions
The rate of climb is the excess power divided by the aircraft's weight: RC = (P_available - P_required) / W. P_available is the power the engine can deliver, P_required is the power needed to hold straight-and-level flight, and W is the weight. The excess power - the difference - is power not being spent fighting drag, and it has nowhere to go but into the aircraft's gravitational potential energy. Dividing it by weight tells you directly how many metres of height the aircraft gains each second.
The rate of climb is the height gained per unit time (m/s or m/min) and is set by excess power. The climb angle is the angle the flight path makes with the horizontal; from sin(gamma) = RC / V it also depends on airspeed V. For the same rate of climb, a slower speed gives a steeper angle. Whether you clear an obstacle just after take-off depends on the climb angle, not the climb rate, and the angle is set by excess thrust rather than excess power.
As altitude increases the air thins, so the power the engine can deliver - the available power - drops. The power required for level flight changes more slowly. As a result the excess power, the difference between the two, keeps shrinking, and so does the rate of climb. The altitude at which the excess power reaches zero is the absolute ceiling, above which the aircraft can climb no further.
The climb gradient is the height gained per unit horizontal distance, expressed as a percentage: gradient = rate of climb / horizontal ground speed x 100 [%]. A gradient of 5%, for example, means the aircraft gains 5 m of height for every 100 m travelled horizontally. Obstacle-clearance rules around airports and instrument departure procedures (SIDs) specify minimum climb gradients (often around 3.3%) as a safety requirement.
Real-World Applications
Airline flight planning: The climb from take-off to cruise altitude affects fuel burn, flight time and airspace congestion. A heavy aircraft (full load, long-haul flight) has less excess power and a lower rate of climb, so it takes longer to reach cruise altitude. Operators build a realistic step-climb plan based on the day's weight, temperature and departure-airport elevation.
Obstacle-clearance limits and departure procedures: Instrument departure procedures (SIDs) specify a minimum climb gradient; an aircraft that cannot meet that gradient cannot depart from that airport on that route. Whether the required gradient can be held even with one engine failed effectively sets the maximum take-off weight for the day. At airports surrounded by mountains, this climb gradient is often the limiting operational constraint.
Fighter energy manoeuvrability: "Specific excess power" (Ps), the excess power divided by weight, is the master measure of a fighter's combat performance. An aircraft with high Ps can climb fast, accelerate fast and gain a better position in a dogfight. During design, performance is assessed by drawing a "Ps diagram" - contours of Ps over a grid of speed and altitude.
Teaching flight mechanics and concept checks: The excess-power method is a starting point for grasping the essence of climb performance before diving into complex aerodynamic models. A simple power-balance calculation like this tool builds intuition for how weight, power and speed affect the rate of climb, before moving on to a more detailed performance analysis (power lapse with altitude, the drag polar). That order is natural for both teaching and practice.
Common Misconceptions and Pitfalls
The biggest confusion is treating rate of climb and climb angle as the same thing. The rate of climb is height gained per unit time (set by excess power), while the climb angle is the steepness of the flight path (set by excess thrust), and the speed for the best rate of climb generally differs from the speed for the best climb angle. At the best-rate-of-climb speed the aircraft climbs "fastest", but a slower speed makes the angle "steeper". To clear an obstacle just after take-off you need a steep angle; to reach cruise altitude in the shortest time you need a high rate of climb. Do not get the objectives mixed up.
Next, assuming the excess power is constant with altitude. This tool fixes the excess power as an input, but on a real aircraft the available power drops with altitude as the air density falls. The required power changes more gently, so the excess power shrinks with altitude and the rate of climb decreases monotonically. The altitude at which the excess power reaches zero is the absolute ceiling. Do not apply a result computed at one altitude to all altitudes.
Finally, failing to distinguish power from thrust. The rate of climb is set by excess power and the climb angle by excess thrust, and the two are linked through speed (power = thrust x speed). A propeller aircraft tends to deliver roughly constant power while a jet tends to deliver roughly constant thrust, and the trend of the optimum climb speed changes accordingly. This tool uses the power-based excess-power method, so its starting point differs from thrust-based discussions of take-off performance - keep that in mind.