Endurance is energy divided by power, and both halves are easy to get wrong
A multirotor flies until the usable energy in the pack runs out. So endurance is one division: usable energy divided by the rate you consume it. Every complication in the subject lives in one of those two quantities, and neither is the number printed on the battery.
The energy side is straightforward once you stop using nameplate capacity. A 5,000 mAh 6S pack holds 5.0 Ah × 22.2 V = 111 Wh on paper, but drawing all of it takes cells below 3.0 V under load and destroys them. Plan on 80% and the pack holds 88.8 Wh. That single correction accounts for a fifth of most optimistic estimates.
The power side is where the physics enters. Hovering costs power because the rotors must throw air downward fast enough that the momentum change supports the aircraft. Momentum theory gives the minimum: power rises with thrust to the power 1.5 and falls with the square root of the disc area. That exponent is the reason a 20% heavier drone loses more than 20% of its flight time, and the square root on area is the reason larger propellers beat faster ones.
If you have a watt meter, skip the estimate. A logged hover current folds in every loss the theory approximates — blade profile drag, motor heating, ESC switching, wiring, tip losses — and it is the number to plan a mission from. The estimate is for aircraft you have not built yet.
Where the hover power expression comes from
Treat each rotor as a disc that accelerates the air passing through it. To hold up a mass m the discs must generate thrust T = m·g. Momentum theory says the ideal power required is T multiplied by the induced velocity through the disc, and that velocity is √(T / (2ρA)). Multiply them and the ideal induced power is T1.5 ÷ √(2ρA).
Read the exponents, because they are the design rules. Power goes as thrust1.5: add 20% to the all-up weight and hover power rises by 1.21.5 = 1.32, a 32% increase, so endurance falls by about a quarter. Power goes as A−0.5: double the total disc area and power falls by a factor of √2 = 1.414, worth 41% more endurance. Nothing else in multirotor design produces gains of that size, which is why endurance airframes have implausibly large propellers.
Two efficiencies convert the ideal into an electrical draw. The figure of merit is the ratio of ideal power to actual shaft power, capturing blade profile drag, tip losses and non-uniform inflow; small multirotor props sit around 0.6–0.7. The drivetrain efficiency covers the motor and ESC together, typically 0.75–0.85 at hover throttle. Divide by both and you have watts at the battery terminals. Divide those by the pack voltage and you have amps, which is what the endurance division needs.
Because momentum theory ignores the airframe entirely, the estimate is a floor on power and therefore a ceiling on time. It says nothing about wind, forward flight, manoeuvring, disturbed inflow from the airframe, or the voltage sag that reduces usable capacity at high draw. Use it to compare configurations and to size a build; use a watt meter to plan a flight.
Worked example: a 1.5 kg quad on 10-inch props with a 6S 5,000 mAh pack
All-up weight 1.5 kg, four 10-inch propellers, a 6S 5,000 mAh LiPo, 80% usable, figure of merit 0.65, motor and ESC 80% efficient, sea-level air at 1.225 kg/m³.
- Usable energy. Pack voltage 6 × 3.7 = 22.2 V. Usable capacity 5.0 × 0.80 = 4.000 Ah. Energy 4.000 × 22.2 = 88.8 Wh.
- Disc area. A 10-inch prop is 0.254 m across, radius 0.127 m, so one disc is π × 0.127² = 0.050671 m². Four of them: 0.202683 m².
- Thrust. 1.5 × 9.80665 = 14.710 N.
- Ideal power. 14.7101.5 = 14.710 × √14.710 = 14.710 × 3.8354 = 56.418. Divide by √(2 × 1.225 × 0.202683) = √0.496573 = 0.704680: 80.06 W.
- Electrical power. 80.06 ÷ (0.65 × 0.80) = 80.06 ÷ 0.52 = 153.97 W.
- Current. 153.97 ÷ 22.2 = 6.935 A.
- Endurance. 4.000 Ah ÷ 6.935 A = 0.5768 h = 34.6 minutes, or 27.7 minutes after holding back a 20% reserve.
- Hover efficiency. 1,500 g ÷ 153.97 W = 9.74 g/W, which is a plausible figure for this class of airframe.
Now add a 500 g camera and gimbal. The weight rises to 2.0 kg, a factor of 1.333, so hover power rises by 1.3331.5 = 1.540 to 237.0 W, current to 10.68 A, and endurance falls to 4.000 ÷ 10.68 × 60 = 22.5 minutes. A third more weight cost 35% of the flight time — the 1.5 exponent at work.
Reading the result, and what to change when it is too short
Check the grams-per-watt figure first, because it is the sanity test on everything else. Well-built multirotors on efficient propellers land between roughly 6 and 12 g/W in hover; heavy-lift machines on large slow discs reach the top of that band and small high-disc-loading racers sit well below it. If the calculator reports 20 g/W, an input is wrong — usually the propeller diameter entered as a radius, or a figure of merit set optimistically high.
If the endurance is too short, the levers are not equally strong. Disc area is the best of them: going from four 10-inch props to four 13-inch props raises the area by (13/10)² = 1.69 and cuts hover power by √1.69 = 1.30, worth 30% more time for no extra energy. Weight is next, and it works against you at the 1.5 power. A bigger battery is the weakest lever of the three, because the extra pack weight partly consumes the extra energy it carries — there is a pack size beyond which endurance stops improving for any given airframe.
Treat the reserve as a hard number rather than a comfort margin. A 20% reserve on the worked example is 6.9 minutes of hover, and that is what covers a diverted landing, a headwind on the way home, or a go-around. The FAA’s Part 107 preflight rule requires you to determine that the aircraft has enough available power for the intended operation; the reserve output is the number that supports that determination.
Finally, remember the estimate assumes still-air hover at the density you entered. Density falls about 3% per 300 m of altitude, and lower density means more induced power for the same thrust — the same aircraft flying a survey at 2,000 m needs roughly 10% more hover power than at sea level. Enter the density for the site rather than the default when it matters.
Endurance against all-up weight for one airframe
| All-up weight | Hover power | Average current | Hover time | Hover efficiency |
|---|---|---|---|---|
| 1.0 kg | 83.8 W | 3.77 A | 63.6 min | 11.93 g/W |
| 1.5 kg | 154.0 W | 6.94 A | 34.6 min | 9.74 g/W |
| 2.0 kg | 237.0 W | 10.68 A | 22.5 min | 8.44 g/W |
| 2.5 kg | 331.3 W | 14.92 A | 16.1 min | 7.55 g/W |
| 3.0 kg | 435.4 W | 19.61 A | 12.2 min | 6.89 g/W |
Tripling the weight from 1.0 to 3.0 kg multiplies hover power by 3^1.5 = 5.196 (83.8 × 5.196 = 435.4) and divides endurance by the same factor. These are ideal-hover figures on a fixed pack; a real 3 kg aircraft would also carry a larger battery, which changes both sides of the division.
This is an estimate of hover, not a flight plan
Momentum theory gives the minimum power to hold an aircraft up in still air. It does not model wind, forward flight, climb, aggressive manoeuvring, propeller wash over the airframe, cold-weather capacity loss, or the voltage sag that reduces the energy actually available at high current. Every one of those makes the real number smaller. Treat the figure as an upper bound for comparing configurations, verify it with a logged hover on a watt meter, and fly to the measured number.
Under 14 CFR Part 107, the remote pilot in command is responsible for determining before each flight that the aircraft has enough available power to operate for the intended time. That determination has to rest on your own logged data for your own airframe, not on a calculator.
Where flight-time estimates go wrong
- Using nameplate capacity. Planning on 100% of a LiPo pack overstates endurance by 25% and damages cells. Use 80%.
- Entering the propeller radius as the diameter. This quadruples the computed disc area and halves the computed power, and it is the most common single input error.
- Forgetting the battery in the all-up weight. On a small quad the pack is often a third of the mass, and the exponent on weight is 1.5.
- Assuming a bigger pack always helps. Extra capacity brings extra mass, and past a point the added hover power cancels the added energy. Test two pack sizes in the calculator with the weights adjusted.
- Quoting hover endurance as mission endurance. Forward flight in wind, climbs and station-keeping all cost more than hover; survey missions commonly consume 20–40% more than the hover figure.
- Ignoring air density. A hot day at altitude can cost 10–15% of hover performance against the sea-level standard day the default assumes.
- Trusting a figure of merit above 0.75. Full-scale helicopter rotors reach that; small plastic multirotor propellers at low Reynolds number do not.
The rest of the flight-planning arithmetic
Endurance sets how much of a survey you can fly on one pack, and the other half of that calculation is how much ground each photo covers — the ground sample distance calculator turns sensor size, focal length and altitude into centimetres per pixel, which combined with the endurance here gives hectares per battery.
On the build side, the same electrical arithmetic recurs throughout: converting between watts, amps and volts is the watts-to-amps conversion, the underlying relation is P = VI, and sizing wiring and shunts from the currents this calculator reports runs through Ohm’s law. If the aircraft carries an actuated payload rather than a fixed camera, the torque that arm or gimbal needs is a servo sizing problem.
For fixed-wing UAS the energy side of this page still applies unchanged, but the power side does not: a wing in cruise is far cheaper than a rotor in hover, and cruise power depends on lift-to-drag ratio and airspeed rather than on disc area. Use the usable-Wh figure here and divide by a measured cruise power instead.