Hong Life CalculatorsUnderstanding the drone flight time calculator — concept and principle
How long can a multicopter hover on one battery? This calculator estimates hover flight time either from the drone's weight and propellers, using momentum theory with a propeller figure of merit and motor efficiency, or from a known average current. It also shows the hover power, current, thrust per rotor and hover efficiency.
How it is calculated
Usable energy (Wh) = capacity (Ah) × voltage × usable share
Weight W = m × 9.80665; disc area per rotor A = π r²
Ideal hover power P = W^1.5 ÷ √(2 ρ A N), ρ = 1.225 kg/m³
Mechanical power = ideal ÷ figure of merit
Electrical power = mechanical ÷ motor and ESC efficiency
Flight time (min) = usable Wh ÷ electrical power × 60; current = power ÷ voltage
- Second method: electrical power = average current × voltage.
The principle
To hover, a rotor must push air downward with momentum equal to the drone's weight every second. Momentum theory shows that pushing a large amount of air slowly takes less power than pushing a little air fast, so bigger propellers are more efficient. The ideal power is the theoretical minimum; real propellers lose energy to drag and swirl, captured by the figure of merit (typically 0.5–0.7), and motors and speed controllers lose more. Dividing the battery's usable energy by the electrical power gives the time.
Worked example
Default inputs: 1,400 g, 4 rotors, 10-inch props, FM 0.6, 75% motor efficiency, 5,000 mAh at 14.8 V, 80% usable.
- Usable energy = 5 × 14.8 × 0.8 = 59.2 Wh.
- W = 1.4 × 9.80665 = 13.73 N; A = π × 0.127² = 0.0507 m².
- Ideal power = 13.73^1.5 ÷ √(2 × 1.225 × 0.0507 × 4) = 72.2 W; mechanical = 72.2 ÷ 0.6 = 120.3 W; electrical = 120.3 ÷ 0.75 = 160.4 W.
- Current = 160.4 ÷ 14.8 = 10.84 A; thrust per rotor = 350 g; efficiency = 1,400 ÷ 160.4 = 8.73 g/W.
- Flight time = 59.2 ÷ 160.4 × 60 = 22.1 minutes (0:22:08).
| Take-off mass including battery (g) | Hover flight time (minutes) |
|---|---|
| 350 | 177.1 |
| 700 | 62.6 |
| 1,050 | 34.1 |
| 1,400 | 22.1 |
| 1,750 | 15.8 |
| 2,100 | 12.1 |
| 2,800 | 7.8 |
How to read the result
This is hover in still air at sea level. Wind, fast forward flight, climbing, cold batteries and altitude (thinner air) all shorten it, and payloads such as gimbals and lights add power. Landing with a reserve is wise, which is why the usable share is below 100%. Comparing g/W across setups shows which propeller and motor combinations are more efficient.
Common mistakes
- Using the full battery capacity instead of the usable share.
- Forgetting the battery's own weight in the take-off mass.
Frequently asked questions
Why do larger propellers give longer flight times?
They move more air more slowly, which needs less power for the same thrust.
What is figure of merit?
The ratio of ideal to actual power for a hovering rotor, typically 0.5–0.7 for small propellers.
Does a bigger battery always help?
It adds energy but also weight, which raises hover power, so the gain diminishes.
Sources: L. Bauersfeld and D. Scaramuzza, "Range, Endurance, and Optimal Speed Estimates for Multicopters", IEEE Robotics and Automation Letters 7(2), 2022 (arXiv:2109.04741) · U.S. Standard Atmosphere, 1976 (sea-level density 1.225 kg/m³)