Watts to Amps and Amps to Watts - How to Calculate Watts
Conversions between electrical units are usually simple and straightforward - take a formula, write down values, and let the calculator do the rest.
However, in real life, things are not always that simple, especially when converting units that require at least one unit to be known. If You wish to know more about converting watts to amps, amps to watts, volt-amps to watts and similar, read carefully...
How to Convert Amps to Watts, Watts to Amps and Other Formulas
Before diving into the math and physics, it is important to know which unit is used for what:
- 'I': current strength, measured in Amps (A),
- 'P': power, measured in Watts (W),
- 'U': potential difference, measured in Volts (V),
- 'E': energy, measured in Joules (J), although sometimes measured in Wh (Watt-Hours),
- 'T': time, measured in seconds (s) and sometimes in hours (h).
In order to convert Amps (A) to Watts (W) and Watts (W) to Amps (A) one must use two different (although similar) formulas, one for Direct Current (DC) and another for Alternate Current (AC):
DC:
P (W) = I (A) * U (V)
AC:
P (W) = I (A) * U (V) * cos α
Note: α is the phase angle between voltage and current - in DC electric systems α=0° (cos 0°=1), while in AC electric systems α depends on the type of load (inductive or capacitive) - this is Effective Power of AC electric system and is expressed by Watts.
Apparent Power of AC systems is expressed in Volt-Amps (never in watts) and is obtained by multiplying Volts and Amps.
In order to simplify things, very often phase shift in AC systems is considered to be 0° - this is acceptable for some quick calculations, but it may not be sufficient for systems with large inductive or capacitive loads.
So, if in order to convert:
- Amps to Watts, one also needs Volts: P (W) = I (A) * U (V)
- Watts to Amps, one also needs Volts: I (A) = P (W) / U (V)
- Volt and Amps to Watts: P (W) = I (A) * U (V)
- Volts to Amps, one also needs Watts: I (A) = P (W) / U (V)
- Amps to Volts, one also needs Watts: U (V) = P (W) / I (A)
- Watt-Hours to Amp Hours, one also needs Volts: E (Wh) = Capacity (Ah) * U(V)
Watts to Amps Chart
The following Watts to Amps chart lists electric currents (given in Amps) of specific loads, depending on the nominal voltage (α=0°, cos 0°=1):
Power (Watts) | Power (HP) | Current @ Nominal Voltage | ||||
12 Volts | 24 Volts | 36 Volts | 120 Volts | 230 Volts | ||
250 W | 0.335 HP | 20.83 A | 10.41 A | 6.94 A | 2.083 A | 1.087 A |
500 W | 0.67 HP | 41.67 A | 20.83 A | 13.89 A | 4.167 A | 2.174 A |
746 W | 1 HP | 62.16 A | 31.08 A | 20.72 A | 6.216 A | 3.243 A |
1000 W | 1.34 HP | 83.33 A | 41.66 A | 27.78 A | 8.333 A | 4.238 A |
1492 W | 2 HP | 124.3 A | 62.16 A | 41.44 A | 12.43 A | 6.487 A |
2000 W | 2.68 HP | 166.6 A | 83.3 A | 55.5 A | 16.66 A | 8.695 A |
2238 W | 3 HP | 186.5 A | 93.25 A | 62.16 A | 18.65 A | 9.730 A |
2984 W | 4 HP | 248.6 A | 124.3 A | 82.88 A | 24.86 A | 12.97 A |
3730 W | 5 HP | 310.8 A | 155.4 A | 103.6 A | 31.08 A | 16.21 A |
5000 W (5 kW) | 6.70 HP | 416.6 A | 208.3 A | 138.8 A | 41.6 A | 21.74 A |
10 kW | 13.40 HP | 833.3 A | 416.6 A | 277.8 A | 83.3 A | 43.48 A |
Note: when calculating these values, we have used 1 HP = 746 watts.
For example: if you have a 36V load that requires 3 HP (~2238 W), that load will draw ~62.16 A of current.
Amps to Watts Chart
The following Amps to Watts chart lists power values given in Watts, depending on the specific current and nominal voltage (α=0°, cos 0°=1):
Current (Amps) | Power @ Nominal Voltage | ||||
12 Volts | 24 Volts | 36 Volts | 120 Volts | 230 Volts | |
1 A | 12 W | 24 W | 36 W | 120 W | 230 W |
2 A | 24 W | 48 W | 72 W | 240 W | 460 W |
5 A | 60 W | 120 W | 180 W | 600 W | 1150 W |
10 A | 120 W | 240 W | 360 W | 1200 W | 2300 W |
25 A | 300 W | 600 W | 900 W | 3000 W | 5750 W |
50 A | 600 W | 1200 W | 1800 W | 6000 W | 11500 W |
100 A | 1.2 kW | 2.4 kW | 3.6 kW | 12 kW | 23 kW |
200 A | 2.4 kW | 4.8 kW | 7.2 kW | 24 kW | 46 kW |
500 A | 6 kW | 12 kW | 18 kW | 60 kW | 115 kW |
1000 A | 12 kW | 24 kW | 36 kW | 120 kW | 230 kW |
For example: if you have a 36V motor that is rated at 50 Amps, its nominal power is 1800 watts.
Constant Current Discharge vs Constant Power Discharge
As the batteries are being discharged, their voltage drops due to the increase in internal resistance. Thus, in order to check how good is the battery, one often has to check both Constant Current Discharge Chart and Constant Power Discharge Chart of the battery.
Note: not all manufacturers provide this information.
For example: The following chart lists constant current discharge values for Renogy RNG-BATT-AGM12-100 battery, given in Amps, measured at 77°F (25°C):
End Voltage (V/Cell) |
End Voltage (V/Battery) |
5 min | 10 min | 15 min | 20 min | 30 min | 45 min | 1 hour | 2 hours | 3 hours | 4 hours | 5 hours | 6 hours | 8 hours | 10 hours | 20 hours |
1.60 | 9.6 | 330.8 | 232.5 | 188.5 | 154.3 | 112.3 | 80.5 | 63.8 | 37.5 | 27.6 | 22.2 | 18.6 | 16.2 | 12.7 | 10.5 | 5.45 |
1.65 | 9.9 | 291.7 | 215.1 | 178.5 | 146.6 | 106.7 | 77.4 | 61.9 | 36.3 | 26.7 | 21.7 | 18.3 | 15.9 | 12.6 | 10.3 | 5.40 |
1.70 | 10.2 | 261.6 | 199.5 | 165.1 | 138.9 | 101.8 | 74.6 | 59.5 | 35.3 | 26.0 | 21.2 | 17.9 | 15.6 | 12.4 | 10.2 | 5.34 |
1.75 | 10.5 | 237.0 | 186.3 | 154.0 | 130.8 | 96.5 | 71.3 | 57.1 | 34.4 | 25.4 | 20.7 | 17.6 | 15.3 | 12.2 | 10.1 | 5.29 |
1.80 | 10.8 | 210.0 | 167.6 | 143.7 | 123.5 | 92.1 | 68.7 | 55.1 | 33.1 | 24.6 | 20.2 | 17.2 | 15.0 | 12.0 | 10.0 | 5.20 |
1.85 | 11.1 | 173.6 | 146.4 | 130.2 | 115.3 | 87.5 | 65.2 | 52.4 | 31.3 | 23.5 | 19.2 | 16.4 | 14.4 | 11.6 | 9.65 | 5.13 |
Also, the following chart lists constant power discharge values for Renogy RNG-BATT-AGM12-100 battery, given in Watts, measured at 77°F (25°C):
End Voltage (V/Cell) |
End Voltage (V/Battery) |
5 min | 10 min | 15 min | 20 min | 30 min | 45 min | 1 hour | 2 hours | 3 hours | 4 hours | 5 hours | 6 hours | 8 hours | 10 hours | 20 hours |
1.60 | 9.6 | 3473 | 2509 | 2070 | 1719 | 1266 | 917 | 734.4 | 426.6 | 316.2 | 255.6 | 215.4 | 187.8 | 148.8 | 123.0 | 64.2 |
1.65 | 9.9 | 3115 | 2348 | 1981 | 1647 | 1211 | 886 | 714.6 | 415.2 | 307.8 | 250.8 | 211.8 | 184.8 | 142.2 | 121.8 | 63.6 |
1.70 | 10.2 | 2825 | 2199 | 1846 | 1570 | 1161 | 858 | 690.0 | 405.6 | 300.6 | 246.0 | 208.8 | 182.4 | 145.8 | 120.6 | 63.0 |
1.75 | 10.5 | 2587 | 2069 | 1732 | 1486 | 1105 | 823 | 664.8 | 396.0 | 294.6 | 240.6 | 205.6 | 179.4 | 144.0 | 119.4 | 62.4 |
1.80 | 10.8 | 2318 | 1873 | 1626 | 1410 | 1060 | 796 | 643.2 | 382.8 | 286.2 | 235.2 | 201.6 | 176.4 | 142.2 | 118.8 | 61.8 |
1.85 | 11.1 | 1935 | 1649 | 1482 | 1323 | 1011 | 758 | 613.2 | 364.8 | 274.2 | 225.0 | 193.2 | 169.2 | 137.4 | 114.6 | 61.2 |
Typically for lead-acid batteries, Renogy AGM battery loses its effective capacity as the discharge current is increased.
As one can see, values in these two charts differ, depending on the discharge type - this is very important for all the loads being powered by the batteries, regardless if they are powered directly or via some power inverter.
For example: the Renogy RNG-BATT-AGM12-100 battery is able to power 205.6 watts load for 5 hours, without the voltage dropping below 10.5 volts - during these 5 hours, both voltage and current changes over time in order to provide required 205.6 watts of power.
Long Story Short: When calculating watts (power), one must know Amps (current) and Volts (voltage). If the electric system is AC (Alternate Current) it is important to know if the load has large impedance/capacitance and how it changes the phase angle (shift) between current and voltage - for quick checks, one may assume that phase shift is 0°, but this is only an approximation.
When converting Wh (energy given in watt-hours) to Ah (capacity given in Amp-hours) and back, one also must know the nominal voltage of the system.
If the power source of the electric system is a lead-acid battery, and the discharge time is shortened, so is the effective capacity of the battery decreased.