Motor Kv & Kt Calculator
Convert motor speed constant Kv, torque constant Kt, and back-EMF constant Ke using the coherent SI motor-constant relationship. The calculator keeps Kv in RPM/V separate from angular speed constant, V/krpm, and V/(rad/s) so datasheet values are easier to compare.
MOT-004 is a constants and reference calculator. It does not model full torque-speed curves, winding resistance, stall current, PWM drive, field weakening, FOC definitions, thermal effects, or manufacturer-specific phase and line conventions.
Engineering tool
Motor Kv & Kt Calculator
Convert motor Kv, Kt and Ke constants, estimate speed from back EMF, calculate torque from current, and check datasheet consistency.
Calculation mode
Parameter panel
Result console
- Torque Constant Kt
- 0.009549297N·m/A
- Torque Constant Kt
- 9.549297mN·m/A
- Torque Constant Kt
- 1.352294oz·in/A
- Speed Constant Kv
- 1000RPM/V
- Angular Speed Constant
- 104.7198rad/s/V
- Back-EMF Constant Ke
- 0.009549297V/(rad/s)
- Back-EMF Constant
- 1V/krpm
Motor Kv & Kt Formula Audit
| Kv Definition | Kv = n / E, where n is mechanical RPM and E is compatible back EMF voltage. |
|---|---|
| Kv Default Unit | RPM/V. |
| Kt Definition | Kt = torque / current. |
| Kt Unit | N·m/A in coherent SI. |
| Ke Definition | Ke = E / omega. |
| Ke Unit | V/(rad/s), equivalent to V·s/rad. |
| Kv → Kt Formula | Kt = 60 / (2πKv) when Kv is in RPM/V. |
| Kt → Kv Formula | Kv = 60 / (2πKt). |
| Kv → Ke Formula | Ke = 60 / (2πKv). |
| Ke → Kv Formula | Kv = 60 / (2πKe). |
| 60/(2π) Constant | Derived from RPM to rad/s conversion; it is not an empirical motor constant. |
| Kt / Ke SI Relationship | Kt in N·m/A and Ke in V/(rad/s) have equal numerical values only under coherent ideal SI definitions. |
| RPM/V → rad/s/V Conversion | Kω = 2πKv / 60. |
| Kv → V/krpm Conversion | Ke,krpm = 1000 / Kv for Kv in RPM/V. |
| Torque / Current Formula | τ = KtI and I = τ/Kt. |
| Speed / EMF Formula | n = KvE and E = n/Kv for compatible back EMF voltage. |
| Terminal Voltage Boundary | Terminal voltage is not exactly back EMF when current creates winding, driver, or brush drops. |
| No-Load Speed Boundary | n≈KvV is only a first-order no-load reference, not an exact loaded-speed prediction. |
| BLDC Phase / Line Boundary | BLDC constants may use phase-to-neutral, line-to-line, peak, RMS, or commutation-specific definitions. |
| Datasheet Consistency Policy | Differences indicate definition/unit review, not an automatic datasheet error. |
| Magnitude Convention | V1 uses positive constants; sign belongs to wiring, rotation, and measurement conventions. |
Formula
Formula reference
Motor Kv, Kt and Ke formulas
The 60/(2π) factor comes from converting RPM to rad/s. Do not use Kt = 1/Kv directly when Kv is in RPM/V.
Kv = n / EKt = τ / IKe = E / ωKt = Ke in coherent SI numerical valuesKt = 60 / (2πKv) for Kv in RPM/VKv = 60 / (2πKt)Kω = 2πKv / 60Ke,krpm = 1000 / KvVariable definitions
- Kv
- speed constant in RPM/V unless otherwise stated
- Kt
- torque constant in N·m/A
- Ke
- back-EMF constant in V/(rad/s)
- n
- mechanical speed in RPM
- ω
- angular velocity in rad/s
- E
- compatible back EMF voltage
- τ
- electromagnetic torque
- I
- motor current
Motor Kv & Kt Formula Audit
| Kv Definition | Kv = n / E, where n is mechanical speed in RPM and E is compatible back EMF voltage. |
|---|---|
| Kv Default Unit | RPM/V. |
| Kt Definition | Kt = τ / I. |
| Kt Unit | N·m/A. |
| Ke Definition | Ke = E / ω. |
| Ke Unit | V/(rad/s). |
| Kv → Kt Formula | Kt = 60 / (2πKv) for Kv in RPM/V. |
| Kt → Kv Formula | Kv = 60 / (2πKt). |
| Kv → Ke Formula | Ke = 60 / (2πKv). |
| Ke → Kv Formula | Kv = 60 / (2πKe). |
| 60/(2π) Constant | The constant is derived from converting RPM to rad/s. |
| Kt / Ke SI Relationship | Kt in N·m/A and Ke in V/(rad/s) are numerically equal only under coherent ideal SI definitions. |
| RPM/V → rad/s/V Conversion | Kω = 2πKv / 60. |
| Kv → V/krpm Conversion | Ke,krpm = 1000 / Kv. |
| Torque / Current Formula | τ = KtI; I = τ/Kt. |
| Speed / EMF Formula | n = KvE; E = n/Kv. |
| Terminal Voltage Boundary | Terminal voltage is not exact back EMF when current is flowing. |
| No-Load Speed Boundary | Kv times supply voltage is only an approximate no-load reference. |
| BLDC Phase / Line Boundary | Phase/line and peak/RMS definitions must match before comparing constants. |
| Datasheet Consistency Policy | Small differences are treated as a convention check, not automatic datasheet failure. |
Worked Examples
| Example | Calculation | Result |
|---|---|---|
| Kv = 1000 RPM/V | Kt = 60 / (2π × 1000) | Kt ≈ 0.0095492966 N·m/A |
| Kv = 1000 RPM/V | Ke = 60 / (2π × 1000) | Ke ≈ 0.0095492966 V/(rad/s) |
| Kt = 0.1 N·m/A | Kv = 60 / (2π × 0.1) | Kv ≈ 95.492966 RPM/V |
| Kv = 100 RPM/V | Kt = 60 / (2π × 100) | Kt ≈ 0.095492966 N·m/A |
| Kv = 500 RPM/V | Kt = 60 / (2π × 500) | Kt ≈ 0.019098593 N·m/A |
| Kv = 1000 RPM/V, E = 12 V | n = Kv × E | n = 12000 RPM |
| 12000 RPM, Kv = 1000 RPM/V | E = n / Kv | E = 12 V |
| Kv = 1000 RPM/V | Kω = 2πKv / 60 | Kω ≈ 104.719755 rad/s/V |
| Kv = 1000 RPM/V | Ke,krpm = 1000 / Kv | Ke = 1 V/krpm |
| Kt = 0.1 N·m/A, I = 5 A | τ = KtI | τ = 0.5 N·m |
| τ = 1 N·m, Kt = 0.1 N·m/A | I = τ/Kt | I = 10 A |
| Kt = Ke = 0.1, ω = 100 rad/s, I = 5 A | E = Keω; τ = KtI | EI = 50 W and τω = 50 W |
| Kv round trip | Kv → Kt → Kv | Original Kv recovered |
| Ke round trip | Kv → Ke → Kv | Original Kv recovered |
| Torque round trip | Kt + current → torque → current | Original current recovered |
| Speed round trip | Kv + speed → EMF → speed | Original speed recovered |
| Kv = 0 | Inverse conversion requires division by Kv | Rejected |
| Kt = 0 | Inverse conversion requires division by Kt | Rejected |
| Ke = 0 | Inverse conversion requires division by Ke | Rejected |
| 1000 mN·m/A | Unit conversion | 1 N·m/A |
| Matching Kv and Kt | Compare entered Kt with expected Kt | 0% difference |
| Mismatched datasheet constants | Difference shown in percent | Status asks user to check definitions |
| RPM/V and Ke formula cross-check | E = RPM/Kv and E = Keω | Same EMF within numeric precision |
| Loaded terminal voltage | Vterminal = E + IR + losses | Do not treat terminal voltage as exact back EMF |
Engineering Notes
Motor Kv
Kv is usually listed in RPM per volt and is most useful as a speed/back-EMF reference.
Speed Constant
A higher Kv means more RPM per volt and a lower ideal torque constant.
Torque Constant Kt
Kt links electromagnetic torque to motor current in a first-order model.
Back-EMF Constant Ke
Ke links generated voltage to angular speed and equals Kt numerically only in coherent SI definitions.
RPM/V
RPM/V must be converted before comparing with SI Ke or Kt.
N·m/A
N·m/A is the SI torque constant unit used by the core formula.
V/(rad/s)
V/(rad/s) differs numerically from V/krpm; both are valid only when labeled clearly.
No-Load Speed
Real no-load speed is usually lower than Kv times supply voltage because current and losses are not zero.
Back EMF
The speed-voltage relation should use back EMF, not loaded terminal voltage.
BLDC
BLDC constants can depend on line/phase, RMS/peak, and commutation definitions.
Brushed DC Motor
Brushed DC constants are often more direct, but brush drop, resistance and saturation still matter.
Phase / Line Convention
Never compare constants from different phase or line definitions without conversion.
Torque Current
τ = KtI estimates electromagnetic torque; shaft torque also includes mechanical loss.
Motor Power Identity
Ideal converted electrical power EI equals ideal converted mechanical power τω when Kt and Ke are coherent.
Common Mistakes
- Using Kt = 1/Kv directly for Kv in RPM/V.
- Forgetting the 60/(2π) conversion factor.
- Mixing Kv in RPM/V with angular speed constant in rad/s/V.
- Confusing V/krpm with V/(rad/s).
- Using terminal voltage as exact back EMF while current is flowing.
- Using supply voltage times Kv as exact no-load speed.
- Saying Kt and Ke have the same units.
- Mixing BLDC phase constants and line constants.
- Mixing RMS and peak current or voltage definitions.
- Comparing BLDC torque constants without checking current convention.
- Using 9.55 as an internal exact constant instead of 60/(2π).
- Trying to invert zero Kv, Kt, or Ke.
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Open CalculatorFAQ
Support reference
FAQ
What is motor Kv?
Motor Kv is the speed constant, commonly expressed as RPM per volt. It relates mechanical speed to compatible back EMF voltage in an ideal no-load reference.
What is motor Kt?
Motor Kt is the torque constant. In SI form it is torque per current, usually expressed as N·m/A.
What is motor Ke?
Motor Ke is the back-EMF constant. In SI form it is expressed as V/(rad/s), which means generated voltage per angular speed.
How do I convert Kv to Kt?
For Kv in RPM/V, use Kt = 60 / (2 pi Kv). The common numerical shortcut is Kt ≈ 9.5493 / Kv.
How do I convert Kt to Kv?
Use Kv = 60 / (2 pi Kt), where Kt is in N·m/A and the resulting Kv is in RPM/V.
Why is Kt not simply 1 divided by Kv?
Kv is commonly listed in RPM/V, while Kt is an SI torque constant. The RPM to rad/s conversion introduces the 60/(2 pi) factor.
Where does 9.5493 come from?
It comes from 60 divided by 2 pi. It is a unit-conversion factor, not an empirical motor constant.
What units should Kv use?
This calculator treats the default Kv as RPM/V. It also supports rad/s/V as an angular speed constant with explicit unit labeling.
What units should Kt use?
Use N·m/A for coherent SI calculations. mN·m/A and oz·in/A can be converted for datasheet convenience.
What units should Ke use?
The SI back-EMF unit is V/(rad/s). Datasheets may also use mV/(rad/s) or V/krpm, which are not numerically identical.
Why are Kt and Ke numerically equal in SI units?
In an ideal coherent SI model, E = Ke omega and torque = Kt current, so converted electrical power E times current equals mechanical converted power torque times omega when Ke and Kt are numerically equal.
How do I calculate torque from motor current?
Use torque = Kt times current. This is electromagnetic torque; real shaft torque can be lower because of losses.
How do I calculate current from required torque?
Use current = torque / Kt. Kt must be greater than zero and expressed in compatible units.
How do I calculate back EMF from RPM?
For Kv in RPM/V, use E = RPM / Kv. Equivalently convert RPM to rad/s and use E = Ke omega.
How do I calculate RPM from back EMF?
Use RPM = Kv times E, where E is compatible back EMF voltage, not necessarily loaded motor terminal voltage.
Can I estimate no-load speed from Kv and voltage?
Yes as a first-order reference: no-load speed is approximately Kv times voltage. Real no-load speed is usually lower because of no-load current, winding resistance, brush loss, iron loss, and friction.
Why might datasheet Kv and Kt not match exactly?
Rounding, measurement conditions, temperature, phase or line definitions, peak or RMS conventions, and current definitions can create differences.
How do BLDC phase and line conventions affect motor constants?
BLDC datasheets may use phase-to-neutral, line-to-line, peak, RMS, sinusoidal, or trapezoidal conventions. Compare constants only after confirming compatible definitions.
Engineering Disclaimer
This calculator uses ideal motor-constant relationships. Verify datasheet definitions, line/phase conventions, RMS/peak values, winding resistance, thermal behavior, motor losses, driver behavior, and measured performance before using results in a production design.