Welcome to our calculation tools

Select one of the categories on the left to begin calculating. Our versatile calculators help with all kinds of electrical and mechanical computations.

⚡ Direct Current (DC) Calculations

Direct Current (DC) is the foundation of many electrical applications. Whether in battery systems, solar technology, or electronic devices – with our DC calculators, you can quickly and precisely calculate all important electrical quantities.

Available Calculations:

Active Power: P = U × I

Calculate electrical power in DC applications

Active Power: P = I² × R

Power calculation via current and resistance

Active Power: P = U² / R

Power calculation via voltage and resistance

Mechanical Power: P = W / t

Calculate mechanical work and power

What is Direct Current?

Direct current refers to a current direction that remains constant and does not alternate. Unlike alternating current, the current always flows in the same direction. Typical applications include batteries, rechargeable batteries, solar cells, and electronic circuits. The calculation of voltage, current, resistance, and power in DC systems follows Ohm's Law and fundamental electrical formulas.

🔄 Alternating Current (AC) Calculations

Alternating Current (AC) is the standard power supply in households and industry. The calculations consider not only voltage and current but also the power factor (cos φ) and phase shift – essential for precise results.

Available Calculations:

Apparent Power: S = U × I

Calculate apparent power in AC systems

Active Power: P = U × I × cos φ

Effective power considering the power factor

Reactive Power: Q = U × I × sin φ

Calculate non-usable reactive power

Power Factor: cos φ = P / S

Ratio of active to apparent power

Reactive Factor: sin φ = Q / S

Ratio of reactive to apparent power

Specifics of Alternating Current

In alternating current, the current direction changes periodically, typically at 50 Hz in Europe. A distinction is made between apparent power (S), active power (P), and reactive power (Q). The power factor cos φ describes the ratio between active and apparent power and is crucial for the efficiency of electrical systems.

🔌 Three-Phase Power Calculations

Three-phase power is the backbone of industrial energy supply. With three phase-shifted alternating currents, it enables efficient operation of electric motors and high-performance systems. Our calculators consider the √3 factor for precise three-phase calculations.

Available Calculations:

Apparent Power: S = U × I × √3

Total power in three-phase systems

Active Power: P = U × I × cos φ × √3

Effective power in three-phase motors

Reactive Power: Q = U × I × sin φ × √3

Reactive power in three-phase systems

Power Factor: cos φ = P / S

Ratio of active to apparent power

Reactive Factor: sin φ = Q / S

Ratio of reactive to apparent power

Why Three-Phase Power in Industry?

Three-phase power consists of three alternating currents shifted by 120°. This enables constant power output and efficient energy transmission. The √3 factor (approx. 1.732) is characteristic of all three-phase calculations. Typical applications include electric motors, industrial plants, and high-voltage transmission with 400V voltage.

📏 Cable Cross-Section Calculations

The correct cable cross-section is crucial for safety and efficiency. Our calculators help you determine the optimal cross-section based on current, length, and voltage drop.

Available Calculations:

DC: A = (2 × I × L) / (K × Δu × U)

Cable cross-section for direct current

AC: A = (2 × I × L × cosφ) / (K × Δu × U)

Cable cross-section for alternating current

Three-Phase: A = (√3 × I × L × cosφ) / (K × Δu × U)

Cable cross-section for three-phase current

Significance of Cable Cross-Section

An undersized cable can lead to overheating and voltage drops, while an oversized cable is unnecessarily expensive. The calculation considers current, cable length, conductivity, and permissible voltage drop.

⚙️ Torque Calculations

Torque is a key parameter for electric motors and drives. Calculate the relationship between power, speed, and torque precisely.

Available Calculations:

Torque: Md = 9550 × P / n

Calculate torque from power and speed

Torque in Electric Motors

Torque indicates the rotational force of a motor and is crucial for the selection of drives. The calculation links power (in kW), speed (in rpm), and torque (in Nm).

🔄 Slip Calculations

Slip describes the difference between the synchronous speed and actual speed of asynchronous motors – an important parameter for motor analysis.

Available Calculations:

Slip: S = (Ns - N) / Ns × 100%

Calculate slip for asynchronous motors

Slip in Asynchronous Motors

Slip indicates by how much percent the rotor lags behind the rotating field. It is crucial for the operating behavior and efficiency of the motor.

💡 Energy Savings Calculator

Calculate the potential savings from replacing old motors with modern, efficient models. Amortization and annual cost savings at a glance.

Available Calculations:

Energy Savings Calculator for E-Motors

Calculate potential savings by replacing old motors

Why Motor Replacement?

Modern motors have significantly better efficiency classes. The calculator shows you how quickly an investment in a new motor pays off through lower energy costs.

⚡ Ohm's Law

The fundamental law of electrical engineering: The relationship between voltage, current, and resistance. Simple and precise calculation of all three parameters.

Available Calculations:

Ohm's Law: U = R × I

Calculate voltage, current, or resistance

Ohm's Law – The Basis of Electrical Engineering

Ohm's Law describes the linear relationship between voltage (U), current (I), and resistance (R). It forms the basis for understanding electrical circuits and is essential for all electrical calculations.

DC Power Calculation
P = U × I

Calculate the supplied electrical power, voltage and current of, for example, DC motors.

P = U × I

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 24 Volt DC motor has a rated current of 33.5 Ampere. What electrical power results from these values?
P = U × I
P = 24 V × 33.33 A
P = 0.8 kW or 800 W

Units of Measurement:
Power P = Kilowatt [kW]
Voltage U = Volt [V]
Current I = Ampere [A]

DC Power Calculation
P = I² × R

Calculate the electrical power, current or resistance.

P = I² × R

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A DC motor has a rated current of 25 Ampere and a resistance of 4.8 Ohm. What electrical power results from these values?
P = I² × R
P = (25 A)² × 4.8 Ω
P = 3 kW

Units of Measurement:
Power P = Kilowatt [kW]
Current I = Ampere [A]
Resistance R = Ohm [Ω]

DC Power Calculation
P = U² / R

Calculate the power, voltage or resistance.

P = U² / R

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 24 Volt DC motor has a resistance of 4.8 Ohm. What electrical power results from these values?
P = U² / R
P = (24 V)² / 4.8 Ω
P = 0.12 kW or 120 W

Units of Measurement:
Power P = Kilowatt [kW]
Voltage U = Volt [V]
Resistance R = Ohm [Ω]

Mechanical Power Calculation
P = W / t

Calculate the mechanical power, work or time.

P = W / t

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A DC motor performs 4500 Joule of electrical work within 30 seconds. What electrical power results from these values?
P = W / t
P = 4500 J / 30 s
P = 0.15 kW or 150 W

Units of Measurement:
Power P = Kilowatt [kW]
Work W = Joule [J]
Time t = Seconds [s]

AC Apparent Power
S = U × I

Calculate the apparent power, voltage or current.

S = U × I

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 230 Volt single-phase AC motor has a rated current of 30 Ampere. What apparent power results from these values?
S = U × I
S = 230 V × 30 A
S = 6.9 kVA

Units of Measurement:
Apparent Power S = Kilovolt-Ampere [kVA]
Voltage U = Volt [V]
Current I = Ampere [A]

AC Active Power
P = U × I × cos φ

Calculate the active power, voltage, current or power factor.

P = U × I × cos φ

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A single-phase 230 V AC motor has a rated current of 3.506 Ampere and a cos φ of 0.93. What electrical power results from these values?
P = U × I × cos φ
P = 230 V × 3.506 A × 0.93
P = 0.75 kW

Units of Measurement:
Active Power P = Kilowatt [kW]
Voltage U = Volt [V]
Current I = Ampere [A]
cos φ = unitless

AC Reactive Power
Q = U × I × sin φ

Calculate the reactive power, voltage, current or sin φ.

Q = U × I × sin φ

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 230 Volt single-phase AC motor has a rated current of 8.56 Ampere and a sin φ of 0.92. What reactive power results from these values?
Q = U × I × sin φ
Q = 230 V × 8.56 A × 0.92
Q = 1.811 kVAr

Units of Measurement:
Reactive Power Q = Kilovolt-Ampere Reactive [kVAr]
Voltage U = Volt [V]
Current I = Ampere [A]
sin φ = unitless

AC Power Factor
cos φ = P / S

Calculate cos φ, active power or apparent power.

cos φ = P / S

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 4.0 kW three-phase motor (or 400V electric motor) has a cos phi of 0.85. What apparent power results from these values?
cos φ = P / S
S = P / cos φ
S = 4.0 kW / 0.85
S = 4.706 kVA

Units of Measurement:
Active Power P = Kilowatt [kW]
Apparent Power S = Kilovolt-Ampere [kVA]
cos φ = unitless

AC Reactive Factor
sin φ = Q / S

Calculate sin φ, reactive power or apparent power.

sin φ = Q / S

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
An AC motor with apparent power of 3.2 kVA has a sin phi of 0.234. What reactive power results from these values?
sin φ = Q / S
Q = S × sin φ
Q = 3.2 kVA × 0.234
Q = 0.749 kVAr

Units of Measurement:
Reactive Power Q = Kilovolt-Ampere Reactive [kVAr]
Apparent Power S = Kilovolt-Ampere [kVA]
sin φ = unitless

Three-Phase Apparent Power
S = U × I × √3

Calculate the apparent power, voltage or current.

S = U × I × √3

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 400 Volt three-phase motor has a rated current of 129.9 Ampere. What apparent power results from these values?
S = U × I × √3
S = 400 V × 129.9 A × √3
S = 90 kVA

Units of Measurement:
Apparent Power S = Kilovolt-Ampere [kVA]
Voltage U = Volt [V]
Current I = Ampere [A]
√3 or 1.73 = unitless

Three-Phase Active Power
P = U × I × cos φ × √3

Calculate the active power, voltage, current or power factor.

P = U × I × cos φ × √3

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 400 Volt three-phase standard motor has a rated current of 25.18 Ampere and a cos φ of 0.86. What electrical power results from these values?
P = U × I × cos φ × √3
P = 400 V × 25.18 A × 0.86 × √3
P = 15.003 kW or 15 kW

Units of Measurement:
Active Power P = Kilowatt [kW]
Voltage U = Volt [V]
Current I = Ampere [A]
cos φ = unitless
√3 or 1.73 = unitless

Three-Phase Reactive Power
Q = U × I × sin φ × √3

Calculate the reactive power, voltage, current or sin φ.

Q = U × I × sin φ × √3

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 400 Volt three-phase standard motor has a rated current of 34.516 Ampere and a sin φ of 0.92. What reactive power results from these values?
Q = U × I × sin φ × √3
Q = 400 V × 34.516 A × 0.92 × √3
Q = 22 kVAr

Units of Measurement:
Reactive Power Q = Kilovolt-Ampere Reactive [kVAr]
Voltage U = Volt [V]
Current I = Ampere [A]
sin φ = unitless
√3 or 1.73 = unitless

Three-Phase Power Factor
cos φ = P / S

Calculate cos φ, active power or apparent power.

cos φ = P / S

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 4.0 kW three-phase motor (or 400V electric motor) has a cos phi of 0.85. What apparent power results from these values?
cos φ = P / S
S = P / cos φ
S = 4.0 kW / 0.85
S = 4.706 kVA

Units of Measurement:
Active Power P = Kilowatt [kW]
Apparent Power S = Kilovolt-Ampere [kVA]
cos φ = unitless

Three-Phase Reactive Factor
sin φ = Q / S

Calculate sin φ, reactive power or apparent power.

sin φ = Q / S

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A three-phase motor with apparent power of 15 kVA has a sin phi of 0.33. What reactive power results from these values?
sin φ = Q / S
Q = S × sin φ
Q = 15 kVA × 0.33
Q = 4.95 kVAr

Units of Measurement:
Reactive Power Q = Kilovolt-Ampere Reactive [kVAr]
Apparent Power S = Kilovolt-Ampere [kVA]
sin φ = unitless

DC Cable Cross-Section
A = (2 × I × L) / (K × Δu × U)

Calculate the cable cross-section, maximum current, maximum cable length, or voltage drop.

A = (2 × I × L) / (K × Δu × U)

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 24 Volt DC motor has a rated current of 2.47 Ampere, a cable length of 28 m, and the voltage drop of the cable is 2%. What cable cross-section results from these values?
A = (2 × I × L) / (K × Δu × U)
A = (2 × 2.47 A × 28 m) / (56 × 0.02 × 24 V)
A = 138.32 / 26.88
A = 5.15 mm²

The next larger suitable cross-section is 6 mm²!

Units of Measurement:
Cross-section A = mm²
Voltage U = Volt [V]
Current I = Ampere [A]
Kappa Copper K = 56 [m / Ω × mm²]
Delta U Δu = %

AC Cable Cross-Section
A = (2 × I × L × cosφ) / (K × Δu × U)

Calculate the cable cross-section, maximum current, maximum cable length, or voltage drop.

A = (2 × I × L × cosφ) / (K × Δu × U)

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 230 Volt AC standard motor has a rated current of 25.18 Ampere, a cos φ of 0.86, a cable length of 72 m, and the voltage drop of the cable is 2%. What cable cross-section results from these values?
A = (2 × I × L × cosφ) / (K × Δu × U)
A = (2 × 25.18 A × 72 m × 0.86) / (56 × 2% × 230 V)
A = 3118.29 / 257.60
A = 12.105 mm²

The next larger suitable cross-section is 16 mm²!

Units of Measurement:
Cross-section A = mm²
Voltage U = Volt [V]
Current I = Ampere [A]
Kappa Copper K = 56 [m / Ω × mm²]
Delta U Δu = %
cos φ = unitless

Three-Phase Cable Cross-Section
A = (√3 × I × L × cosφ) / (K × Δu × U)

Calculate the cable cross-section, maximum current, maximum cable length, or voltage drop.

A = (√3 × I × L × cosφ) / (K × Δu × U)

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 400 Volt three-phase asynchronous motor has a rated current of 25 Ampere, a cos φ of 0.89, a cable length of 94 m, and the voltage drop of the cable is 2%. What cable cross-section results from these values?
A = (√3 × I × L × cosφ) / (K × Δu × U)
A = (√3 × 25 A × 94 m × 0.89) / (56 × 2% × 400 V)
A = 3622.48 / 448
A = 8.09 mm²

The next larger suitable cross-section is 10 mm²!

Units of Measurement:
Cross-section A = mm²
Voltage U = Volt [V]
Current I = Ampere [A]
Kappa Copper K = 56 [m / Ω × mm²]
Delta U Δu = %
cos φ = unitless
√3 or 1.732 = unitless

Torque Calculation
Md = 9550 × P / n

Calculate the torque, power, or speed of a motor.

Md = 9550 × P / n

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A standard three-phase motor has a rated speed of 1420 revolutions and a mechanical output power of 15 kW at the motor shaft. What is the motor torque at rated speed?
Md = 9550 × P / n
Md = 9550 × 15 kW / 1420 min⁻¹
Md = 100.88 Nm

For your information: This calculator is only suitable for electric motors without gearboxes!

Units of Measurement:
Torque Md = Newton-meter [Nm]
Power P = Kilowatt [kW]
Speed n = Revolutions per minute [min⁻¹]

Slip Calculation
S = (Ns - N) / Ns × 100%

Calculate the slip, synchronous speed, or rotor speed of an asynchronous motor.

S = (Ns - N) / Ns × 100%

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
An electric motor with a synchronous speed of 1500 rpm shows on its nameplate a speed indication of 1450 revolutions. What slip results from these values?
S = (Ns - N) / Ns × 100%
S = (1500 rpm - 1450 rpm) / 1500 rpm × 100%
S = 3.33%

Units of Measurement:
Slip S = Percent [%]
Speeds = Revolutions per minute [min⁻¹]

Energy Savings Calculator for E-Motors

Calculate the energy savings and payback period when replacing an old motor with an energy-efficient motor.

✅ Result:

Example Calculation:
The calculator shows the annual energy savings in kWh, the cost savings in € and the payback time in years.

Explanation:
The calculator shows the annual energy savings in kWh, the cost savings in € and the payback time in years.

Ohm's Law
U = I × R

Calculate voltage, current, or resistance according to Ohm's Law.

U = I × R

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 12 V circuit has an ohmic load with a resistance of 3 Ohm. What current results from these values?
U = I × R
I = U / R
I = 12 V / 3 Ω
I = 4 A

Units of Measurement:
Voltage U = Volt [V]
Current I = Ampere [A]
Resistance R = Ohm [Ω]