BLDC motor calculator: winding, Kv and resonance
From the slot/pole combination to the speed: the tool shows the winding scheme as an animation, checks whether the winding is balanced and estimates Kv, torque and resistance from turns, wire and magnets. Plus the frequencies at which resonances can occur.
Free, no account needed
1. Winding
Enter slots (= teeth with a coil) and magnets. The calculation assumes a three-phase concentrated (tooth-coil) winding, as used in almost all outrunners and many wind generators.
How the motor turns: the controller always energizes two phases (bright), the third is open (faded). It switches every 60° electrical; six steps make one electrical revolution. With 7 pole pairs the rotor only needs 1/7 of a revolution for this. Schematic, not to scale.
Winding guide
How to wind the coils: the stator unrolled, tooth by tooth. “Step by step” tells you for each coil which tooth, which direction and where the wire goes next.
- Before winding, deburr the tooth edges and insulate the slots (slot insulation paper or powder coating), otherwise the wire enamel chafes through.
- Wind all coils with the same number of turns, tightly and in layers, without crossing.
- Route all jumper wires on the same end face and secure them there (thread, varnish or glue).
- After each phase, measure the resistance from start to end. The three phase windings must be equal.
- Finally check the insulation: no continuity between winding and stator laminations.
- On the first run, watch the no-load current. If it is clearly higher than usual, a coil is usually wound the wrong way round.
Connection: star or delta
How the three finished phase windings are connected. The connection chosen above in section 3 is highlighted.
Join the ends U2, V2 and W2 together and insulate them: this is the star point, it is not connected. The starts U1, V1 and W1 go to the three leads to the ESC. The order does not matter; swapping two leads reverses the direction of rotation.
Connect U1 with W2, V1 with U2 and W1 with V2, like the links on a motor terminal board per IEC 60034-8. Each of the three junctions gets one lead to the ESC. Other assignments (U1 with V2 …) also form a delta; only the direction of rotation may differ.
2. Good combinations
Balanced magnet counts for 12 slots with a winding factor of 0.7 or more, best first. Proven combinations have a winding factor of 0.93 or more and balanced radial forces.
| Combination | Winding factor | Cogging steps/revolution | Radial forces | q | |
|---|---|---|---|---|---|
| 12N14P | 0.933 | 84 | balanced | 0.286 | |
| 12N10P | 0.933 | 60 | balanced | 0.400 | |
| 12N16P | 0.866 | 48 | balanced | 0.250 | |
| 12N8P | 0.866 | 24 | balanced | 0.500 |
3. Motor data from turns and magnets
From the winding and dimensions the tool estimates Kv, torque constant and resistance. Useful for planning before winding and for comparing variants.
| No-load speed at 12 V | 3,653 rpm |
| Torque at 3 A | 0.0941 N·m |
| Current density in the wire | 7.64 A/mm² |
| Copper losses at 3 A | 2.84 W |
| Fundamental of the air-gap flux density B₁ | 0.867 T |
Estimate, typically ±20 %. Leakage, saturation and magnet shape depend on the design. You measure the exact Kv on the finished motor (see notes).
4. Frequencies and resonance
At which speed does which frequency hit a natural frequency? The values apply at the speed from section 3.
| at 3,653 rpm | |
| Rotational frequency (mechanical) | 60.9 Hz |
| Electrical frequency | 426 Hz |
| Commutations per second | 2.56 kHz |
| Cogging frequency | 5.11 kHz |
Measure and connect: coil, capacitor, Kv
For all measurements the motor is disconnected from the ESC. “Two motor terminals” means: two of the three wires, e.g. U1 and V1; the third stays free.
Generator (sine, 1–5 V) → resistor R (e.g. 100 Ω) → motor terminal U1 → through the winding → motor terminal V1 → capacitor → back to the generator. The oscilloscope measures across R. Sweep the frequency slowly: where the voltage across R is highest, that is f₀.
Solder the capacitor directly to two motor terminals (e.g. U1 and V1). Connect this resonant circuit to the generator via R (e.g. 1 kΩ). The oscilloscope measures across the two motor terminals: at f₀ the voltage there is highest. Without a capacitor, this finds the self-resonance of the winding.
Turn the shaft steadily with a drill or cordless screwdriver. The oscilloscope between two terminals shows the peak voltage and the frequency f. Speed = 60 × f ÷ pole pairs (or use a tachometer). Kv = speed ÷ peak voltage. A multimeter shows the RMS value: then Kv = speed ÷ (RMS value × 1.41).
Measure the resistance between all three pairs; the values must be equal, otherwise a coil has a shorted turn or a solder joint is bad. For values below 1 Ω, first short the test leads together and subtract that value, or more accurately: feed in 1 A and measure the voltage directly at the terminals (four-wire (Kelvin) measurement).
How to find the resonance
- Electrically with a capacitor: measure inductance L between two terminals, choose a capacitor. f₀ = 1 ÷ (2π √(L·C)) is shown above, as is the speed at which the electrical frequency reaches f₀.
- Confirm by measurement (circuit diagrams above): in the series resonant circuit the voltage across resistor R is highest at f₀, in the parallel resonant circuit the voltage across the resonant circuit itself. Sweep the generator frequency slowly and look for the maximum.
- Self-resonance of the coil: even without a capacitor, every winding resonates with its own capacitance, usually in the range 100 kHz to a few MHz. Measure the same way as the parallel resonant circuit, just without the capacitor; this frequency limits how fast you should switch.
- Mechanically: cogging frequency and rotation frequency can excite the housing, mount or mast. Measure the natural frequency by tapping and using a microphone (spectrum app), enter it above and avoid the speed shown.
- What shifts the resonance: more turns increase L (roughly with the square), more capacitance lowers f₀, more pole pairs raise the electrical frequency at the same speed, a stiffer mount raises the mechanical natural frequency.
5. As a generator
For wind turbines and bicycle dynamos: open-circuit voltage at the speed from section 3, without load.
| at 3,653 rpm | |
| Peak voltage between two terminals | 12 V |
| RMS value | 8.49 V |
| DC voltage after bridge rectifier | 10.1 V |
6. Rewinding
Same motor, different number of turns or connection: this is how Kv changes. Applies with the same copper fill of the slots.
Formula
Slot star: coil k has the angle θk = k · p · 360° ÷ N. Winding factor kw = kp · kd with kp = sin(p · 180° ÷ N). Cogging: LCM(N, 2p). Back-EMF per phase: Ke = N_phase · kw · B₁ · D · L with B₁ = 4/π · B · sin(α · 90°); star: Ke(line) = √3 · Ke. Kv = 60 ÷ (2π · Ke(line)), Kt ≈ 60 ÷ (2π · Kv). f_el = rpm ÷ 60 · p. R = ρ · l ÷ A. LC: f₀ = 1 ÷ (2π √(L · C)).
Example
12 slots, 14 magnets, double-layer: scheme AabBCcaABbcC, winding factor 0.933, 84 cogging steps per revolution. With 10 turns per tooth in star, Ø 28 mm × 20 mm and 0.7 T this gives about 300 rpm per volt; two 0.5 mm wires in parallel have 0.105 Ω per phase. At 12 V the motor runs at about 3650 rpm without load, the electrical frequency is then 426 Hz.
Notes
- The tool calculates concentrated (tooth-coil) windings (each coil around one tooth, q ≤ 0.5). It does not calculate the distributed windings of large industrial motors.
- Kv from the geometry is an estimate (about ±20 %). To measure it exactly: spin the motor with a drill, measure the speed and the peak voltage between two terminals. Kv = speed ÷ peak voltage.
- The resistance applies at 20 °C without leads. Warm copper has 0.39 % more resistance per degree.
- Neodymium magnets permanently lose strength above their temperature limit (often 80 °C for N grades). During assembly they can pinch fingers; keep tools away.
- Scheme, animation and EMF curve are idealized (trapezoid, block commutation). Field-oriented control (FOC) uses sinusoidal currents, but the combination and the winding factor apply just the same.
- Above 60 V DC and with rotating rotors there is a risk of injury. Generators produce voltage as soon as they turn, even when disconnected.