What does the motor constant k represent?

In SI units, k is both the back-EMF constant and torque constant: k_e = k_t = k.

Can I enter speed in RPM?

Yes. Select RPM, and the calculator converts the value to rad/s for the calculations.

What formulas does the calculator use?

It uses E = k·ω for back-EMF, T = k·I for torque, and P = T·ω = E·I for mechanical power.

What units are used for the results?

Back-EMF is returned in volts, torque in N·m, speed in rad/s and RPM, and mechanical power in watts.

Can the armature current be zero?

Yes. A zero current produces zero torque and zero mechanical power, while back-EMF still depends on speed and k.

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DC Motor Back-EMF & Torque Calculator (E=kω, T=kI)

Compute the back-EMF and electromagnetic torque of a DC motor from its machine constant: E=k·ω, T=k·I. In SI units the back-EMF constant equals the torque constant (k_e=k_t=k, V·s/rad=N·m/A). Also returns the mechanical (air-gap) power P=T·ω=E·I. Speed accepted in rad/s or RPM.

Execution

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2 examples

k=0.1, ω=100 rad/s, I=5 A → E=10 V, T=0.5 N·m, P=50 W

E = k·ω = 0.1·100 = 10 V. T = k·I = 0.1·5 = 0.5 N·m. P_mech = T·ω = E·I = 50 W. Note E·I = 10·5 = 50 W confirms the electromechanical power balance.

{"result":"DC motor back-EMF & torque. k=0.1 V·s/rad (N·m/A), ω=100 rad/s (954.9297 RPM), I=5 A. E = k·ω = 10 V. T = k·I = 0.5 N·m. P_mech = T·ω = E·I = 50 W.","metadata":{"input":{"k":0.1,"speed":100,"speedUnit":"rad_s","current":5},"result":{"motorConstant_k":0.1,"speed_rad_s":100,"speed_rpm":954.9297,"armatureCurrent_A":5,"backEmf_V":10,"torque_Nm":0.5,"mechanicalPower_W":50}}}

k=0.05, n=3000 RPM, I=10 A → E≈15.71 V, T=0.5 N·m, P≈157.08 W

ω = 3000·2π/60 ≈ 314.159 rad/s. E = 0.05·314.159 ≈ 15.708 V. T = 0.05·10 = 0.5 N·m. P_mech = T·ω = 0.5·314.159 ≈ 157.08 W.

{"result":"DC motor back-EMF & torque. k=0.05 V·s/rad (N·m/A), ω=314.1593 rad/s (3000 RPM), I=10 A. E = k·ω = 15.708 V. T = k·I = 0.5 N·m. P_mech = T·ω = E·I = 157.0796 W.","metadata":{"input":{"k":0.05,"speed":3000,"speedUnit":"rpm","current":10},"result":{"motorConstant_k":0.05,"speed_rad_s":314.1593,"speed_rpm":3000,"armatureCurrent_A":10,"backEmf_V":15.708,"torque_Nm":0.5,"mechanicalPower_W":157.0796}}}

Inputs

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5 options

SettingsAdjust formats, ranges, numbers, and modes.5

Motor Constant k (V·s/rad = N·m/A)numberRequiredMachine constant k. In SI units k_e (V·s/rad) = k_t (N·m/A) = k.Angular Speed ωnumberRequiredRotor angular speed in the selected unit (rad/s or RPM).Speed UnitselectOptionalArmature Current I (A)numberRequiredArmature current I (A). May be 0 (then torque and power are 0).Decimal PlacesnumberOptional

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Samples

DC Motor Back-EMF & Torque Calculator (E=kω, T=kI)

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Use cases

Examples

1. Estimate back-EMF and torque at 100 rad/s

2. Calculate motor values from 3000 RPM

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