Drone Motor & Battery Calculator – Thrust, TWR, Flight Time Estimator

Example result for the above configuration:

• Total Thrust ≈ 2,800–3,200 gf | TWR ≈ 5.8:1
• Hover Throttle ≈ 41% | Hover Current ≈ 20 A total
• Flight Time ≈ 3.5 min (hover) | C-Rating: Safe (20A / 112A)

This calculator uses two different voltage references because thrust and flight-time calculations represent physically different questions.

Thrust / TWR / RPM — full-charge voltage (fixed 4.2 V/cell)

V_thrust = cell_count × 4.2

• Motor manufacturer thrust tables are measured at full charge. A 4S battery is listed as "14.8V" (= 4 × 3.7V nominal) but is fully charged at 4 × 4.2V = 16.8V when thrust data is recorded [R-V1, R-V2].
• The load-RPM factor 0.88 is designed to work with this full-charge baseline. Applying it on top of 3.7V would double-penalise RPM by ~25% [R-V1, R6].
• This basis makes computed thrust and TWR directly comparable to manufacturer datasheets.

Flight Time — average discharge voltage (default 3.7 V/cell, user-adjustable)

V_avg = cell_count × avg_cell_v (default 3.7 V)

• LiPo cells provide 4.2V briefly at full charge, then settle at ~3.7V for most of the discharge cycle, dropping to ~3.5V near landing [R-V1, R-V2].
• EveryDrone.io and other drone calculators use the average discharge voltage (3.5–3.7V) for energy estimation, not peak voltage [R-V3, R-V4].
• Advanced mode: set Avg Cell Voltage to 3.5V for a conservative estimate, 3.8V for HV LiPo, or 3.6V for Li-ion cells.

energy_correction = V_avg / V_thrust (e.g. 3.7 / 4.2 ≈ 0.88)

• This factor is applied to flight time to account for the lower average energy delivered compared to the full-charge thrust basis.

RPM_load = KV × V_thrust × load_factor(D)

RPS = RPM_load / 60

load_factor(D) — propeller-size-dependent:

• D ≤ 5.5" : 0.88 — FPV range, calibrated against EMAX/T-Motor 2207 bench data
• 5.5" < D ≤ 12" : linear 0.88 → 0.76 — transitional (7", 9", 10" photo/cinematic props)
• D > 12" : 0.76 — floor for large props (12"+ agricultural / heavy-lift)

Physical basis [R5]: The motor torque equilibrium in a BLDC motor satisfies:

Q_motor = K_t × (V − K_e × ω) / R_m ≡ Q_prop = Cq × ρ × n² × D⁵

• Because propeller aerodynamic torque scales as D⁵ (Leishman [R5], Ch. 3), larger propellers impose substantially heavier loads per revolution. For a fixed motor KV and voltage, this pushes the equilibrium operating point to a progressively lower fraction of no-load RPM as D increases.
• Bench data (Tyto Robotics, MiniQuadTestBench) confirms loaded RPM is ~85–92% of no-load for 5" FPV props and falls to ~75–80% for 9–10" props at typical operating voltages.
• ⚠ For propellers larger than 12" paired with motors below ~400 KV, the simplified load-factor approximation increasingly underestimates the aerodynamic loading; see Accuracy Roadmap Level 3 for the motor torque-curve model required for this regime.

Calibration reference (all three validated simultaneously):

• 2550 KV / 4S / 5×4.6 / 3-blade → load_factor = 0.88 → ~814 gf (real: ~820 gf, error < 1%)
• 1700 KV / 4S / 7×3.5 / 2-blade → load_factor ≈ 0.852 → ~1,380 gf (real: ~1,200–1,450 gf)
• 920 KV / 4S / 9×4.5 / 2-blade → load_factor ≈ 0.815 → ~1,280 gf (real: ~1,000–1,300 gf)

T [gf] = Ct × mach_correction × RPS² × D⁴

Ct = 5×10⁻⁶ × blade_factor × pitch_correction × size_correction

• This is the standard dimensional form of actuator-disk / blade-element thrust theory [R5]. The D⁴ dependence comes from dimensional analysis: T [N] = Ct_dim × ρ × n² × D[m]⁴, converted to gf/inches units. UIUC database [R1] provides the population-average Ct values that calibrate the base coefficient.
• Pitch enters the formula only through pitch_correction inside Ct — it must not be multiplied again as a separate term. Earlier versions of this calculator incorrectly multiplied by pitch a second time (T × P), which is physically invalid [R1].

Base coefficient derivation:

T [N] = Ct_dimensionless × ρ × n² × D[m]⁴ → Ct_dim [gf] = Ct_dimensionless × 5.196×10⁻⁵

• The standard SI formula is converted to gf/inches units by multiplying by (0.0254)⁴ m⁴/in⁴ and 101.972 gf/N.
• Typical UIUC J=0 values: Ct_dimensionless ≈ 0.09–0.12 → Ct_dim ≈ 5×10⁻⁶ [R1, R2]. This replaces the previous incorrect value of 7×10⁻⁷, which corresponded to Ct_dimensionless = 0.013 — well below any reported UIUC value for real propellers.
• Individual propellers vary ±20–30% around this average [R4]. Population-level accuracy is ±20%.

blade_factor — Ct increases with blade count. Source: empirical analysis of 170+ propellers [R4]:

• 2-blade: × 1.00 (baseline)
• 3-blade: × 1.15 (+15% Ct; efficiency decreases)
• 4-blade: × 1.30 (+30% Ct; further efficiency decrease)

pitch_correction — UIUC propeller static-thrust data (J = 0) shows Ct peaks in the moderate P/D range (0.4–0.8) and decreases at both extremes. Dantsker et al. (2022) [R2] Fig. 7–9: at J=0 the variation from P/D 0.43 to P/D 0.67 is within ±4% of Ct, well below the ±20–30% population scatter. The previous boost of ×1.05 for P/D < 0.6 was not supported by this data.

• P/D < 0.40: × 0.95 — near-flat blades, Ct slightly below optimum [R1, R2]
• 0.40–0.80: × 1.00 — optimal static-thrust zone (baseline) [R1, R2]
• 0.80–1.0: × 0.95 — incipient stall, Ct decreasing [R2]
• 1.0–1.2: × 0.90 — partial stall [R2]
• P/D ≥ 1.2: × 0.85 — deep stall [R2]

size_correction — Ct is not constant across diameters. Reynolds number effects and tip-loss fraction both increase with propeller size, causing Ct to decrease [R3, R4]. Three explicit segments (D > 28" now hits the hard floor directly, fixing an earlier boundary bug):

• D ≤ 6 in: × 1.00 (baseline — small FPV props)
• 6–18 in: linear interpolation 1.00 → 0.55 [R3, R4]
• 18–28 in: linear interpolation 0.55 → 0.35 [R2]
• D > 28 in: × 0.20 hard floor (large agricultural rotors) [R2]

mach_correction — Blade tip compressibility effect. At tip Mach > 0.50, shock-wave formation progressively reduces the effective static Ct:

tip_speed [m/s] = π × D[m] × RPS

mach_tip = tip_speed / 343 (speed of sound at sea level)

mach_correction = 1.0 → 0.40 (linear, Mach 0.50 → 0.85)

• High-KV FPV motors (e.g. 2550 KV on 4S with 5" props) reach Mach 0.70–0.75 at the blade tip, reducing effective Ct by ~35–40%.
• Slow-flying cinematic or cargo drones (e.g. 400 KV on 6S with 10" props) stay below Mach 0.40 — no correction applied.
• Calibration reference: 2550 KV / 4S / 5×4.6 3-blade → tip Ma ≈ 0.73 → correction ≈ 0.60 → ~820 gf/motor, consistent with EMAX / T-Motor 2207 bench data.

⚠ Joint-Calibration Note: Ct_base (5.0e-6) and mach_correction are jointly calibrated and cannot be modified independently. Ct_base represents the theoretical uncompressed thrust coefficient valid at sub-Mach-0.50 tip speeds, derived from UIUC dimensionless Ct ≈ 0.096 [R1]. The mach_correction slope and floor are then tuned so the product Ct_base × mach_correction reproduces real bench-test thrust at FPV operating tip speeds (Ma 0.70–0.85).

• Pre-correction thrust (= Ct_base × blade_factor × pitch_correction × size_correction × rps² × D⁴) is an intermediate calculation step — not a physically meaningful quantity on its own.
• Post-correction thrust (× mach_correction) is what is validated against motor bench data. Only this value should be compared with real-world measurements.
• Changing Ct_base without recalibrating mach_correction — e.g. to 6.8e-6 as sometimes suggested — would over-estimate thrust by ~35–70% for typical FPV configurations. Both parameters must be re-validated together against the same reference data if either is adjusted.

TWR = T_total / W_total

T_total = T_single × N_motors

• TWR < 1.5: unable to take off (Danger)
• TWR 1.5–2.0: marginally flyable but difficult to control (Danger)
• TWR 2–4: cargo, cinematic, long-range (adequate)
• TWR 4–8: freestyle / sport range (good)
• TWR > 10: racing / acrobatic — verify inputs (Warning)

throttle_hover [%] = √(1 / TWR) × 100

• Derived from the relationship: thrust ∝ throttle² (standard brushless motor model).
• At hover: T_total = W_total, so throttle_hover = √(W / T_max) = √(1/TWR).
• Example: TWR = 6 → throttle_hover = √(1/6) × 100 ≈ 40.8%
• Hover throttle > 70% leaves insufficient headroom for manoeuvres or wind gusts (Warning).

I_hover_per_motor = I_max × (T_hover / T_max)^1.2

T_hover_per_motor = W_total / N_motors

I_hover_total = I_hover_per_motor × N_motors

P_hover [W] = I_hover_total × V_thrust

• Derivation: Actuator-disk (momentum) theory gives P_hover ∝ T^(3/2), so I ∝ (T/T_max)^1.5 at constant voltage and efficiency [R8].
• However, propeller Figure of Merit (FM) decreases at partial load relative to the design point: FM_hover ≈ FM_max × (T_hover/T_max)^0.3 (de Angelis et al. [R8], Tyto bench data [R7]). Dividing out the FM variation:
• I_hover/I_max = (T_hover/T_max)^1.5 / (T_hover/T_max)^0.3 = (T_hover/T_max)^1.2
• The exponent 1.2 lies between the ideal (1.5) and a purely linear heuristic (1.0), capturing partial-load efficiency losses. It is validated against bench data: TWR 6.15 → hover current ≈ 3.0 min flight on 4S 1300 mAh (real: 3–5 min); TWR 7.4 → ≈ 15 min on 7" 3000 mAh (real: 10–18 min).
• Previous approach — I_hover = I_max × (T/T_max)^1.0 — overestimated hover current by 20–40% on high-TWR builds, leading to pessimistic flight-time estimates.
• Voltage basis for P_hover: I_hover is computed from T_max, which is derived at V_thrust (4.2 V/cell full-charge basis). The flight-time formula implies P_hover = I_hover × V_thrust — rearranging t = (C_Ah × V_eff) / P_hover × 60 with V_eff ≈ V_avg confirms this. Using V_avg instead would mix two different voltage reference frames and understate hover power by ≈ 12% relative to the energy balance in the flight-time calculation. [R8]

I_max_battery [A] = C_rating × capacity [Ah]

• Example: 1500 mAh, 75C → max discharge = 1.5 × 75 = 112.5 A
• Danger: Full-throttle current (I_max × N) > I_max_battery — risk of thermal runaway or fire.
• Warning: Sustained 75%-throttle current within 10% of battery limit — tight margin for extended high-throttle segments.
• ⚠ Manufacturer C-ratings are often optimistic. Applying a 0.8 safety factor to rated C is a common community practice.

t_flight [min] = (capacity [Ah] × usable_ratio / I_hover) × (V_eff / V_thrust) × 60

V_eff = V_avg − I_hover_total × R_pack (voltage sag; V_eff = V_avg when R_pack not entered)

• Based on the hover-endurance formula from multirotor sizing analysis [R8], extended with an energy-correction factor and optional voltage-sag term.
• Energy correction V_eff / V_thrust: I_hover is derived at full-charge voltage (4.2 V/cell). Maintaining the same hover thrust at the lower average discharge voltage (≈ 3.7 V/cell) requires proportionally more current (P = T^1.5/η is constant; lower V → higher I). This correction is necessary and is not a double-count of the voltage split. [R-V3, R-V4]
• Voltage sag (Advanced mode): when pack resistance R_pack [mΩ] is provided, V_eff = V_avg − I_hover × R_pack, following the battery internal-resistance model [R9]. A sag of 0.2–0.4 V is typical for 4S LiPo under 20–40 A hover load, reducing estimated flight time by 3–8%.
• usable_ratio (default 80%) limits depth of discharge to protect LiPo lifespan. Landing at ≈ 3.5 V/cell (≈ 20% remaining) is the standard safety margin.
• For active FPV flight, multiply the estimate by 0.5–0.7. For smooth cinematic flight, 0.7–0.85 is realistic.
• Example (no sag): 1500 mAh, 0.8 usable, 18 A hover (T^1.2 model), 4S → t = (1.5 × 0.8 / 18) × (14.8/16.8) × 60 ≈ 3.52 min

• Thrust model: T = Ct × n² × D⁴ with UIUC-calibrated base coefficient, blade-count, pitch-ratio, and size corrections [R1–R5].
• Propeller-size-dependent load-RPM factor: 0.88 (5" FPV) → 0.76 (12"+), derived from BLDC torque balance and D⁵ aerodynamic load scaling [R5, R6].
• Mach tip-speed compressibility correction (linear 1.0 → 0.40 from Ma 0.50 → 0.85) [R6].
• FM-corrected hover current: I_hover ∝ (T_hover/T_max)^1.2 [R7, R8].
• Voltage-sag correction (optional, Advanced mode): V_eff = V_avg − I × R_pack, floor at max(cells × 3.0 V, V_avg × 0.75) [R9].
• Expected accuracy: ±10–20% thrust for 5–10" props, ±20–30% for 10"+ props; ±15–25% flight time — suitable for design comparison and configuration screening.
• Structural note: Ct_base and mach_correction are jointly calibrated — they cannot be adjusted independently. Ct_base = 5.0e-6 is the theoretical UIUC J=0 coefficient; for FPV builds operating at tip Mach 0.70–0.85, the Mach correction (~0.40–0.60) brings Ct_effective down to ≈ 2.0–3.0e-6. Any future improvement to these parameters must be validated as a pair against motor bench-test data.

• Replace the analytic Ct formula with a lookup table of (diameter, pitch, blade-count, RPM) → (Ct, Cq) from UIUC Vols 1–4 [R1] and supplemental FPV-prop databases.
• Bilinear interpolation between the nearest RPM and pitch tabulated points.
• Removes pitch-correction and size-correction heuristics in favour of measured data.
• Expected accuracy: ±10–15% thrust for prop models covered by the database.
• Implementation: embed the UIUC database as a static Rust array compiled into the WASM binary (≈ 200–500 kB).

• Motor model: torque-speed curve (Q vs ω) derived from motor constants (Kv, R_m, iron-loss coefficient). Maps operating RPM to actual current and efficiency.
• Voltage sag: iterative solve for V_eff = V_oc − I × R_pack until thrust = hover requirement (currently single-pass approximation).
• Figure of merit as a function of RPM / disk loading (not a fixed exponent).
• Data source: Tyto Robotics motor-database curves, T-Motor / EMAX published datasheets.
• Expected accuracy: ±5–10% — comparable to eCalc for well-characterised motor+prop combinations.
• Implementation: significantly higher complexity; requires per-motor constant tables and iterative hover-point solver.