Watts to Amps, Amps to Watts, Amp Hours (Ah) to Watts, Watts to Amp Hours (Ah) - Units Conversions, Formulas, and Charts
Units conversions like watts to amps, amps to watts, ah to watts, watts to ah and similar are very important not only when planning and dimensioning future electrical systems, but also when analyzing and testing current ones.
Although math and physics regarding these units are relatively simple and straightforward, one must be very careful - there are many opportunities for errors and these errors may be sometimes rather costly ...
And, sorry about the math ... :)
On this page:
- Quick Explanation About Units
- Watts to Amps and Amps to Watts Formula
- Watts to Amps and Amps to Watts Examples
- Motor Horsepower (HP) to Amps
- Amp Hours (Ah) to Watts and Watts to Amp Hours (Ah) Formula
Quick Explanation About Units
Before diving into the math behind all of these conversions, it is important to explain what is what:
- Watts (W) describes the power/strength of a device like motor, winch, battery and similar,
- Horsepower (HP) is an obsolete power measurement unit. The best of all there are more HP definitions/types, but two of them are the most important:
- the mechanical/imperial horsepower, which is about 745.7 watts (~746 watts),
- the metric horsepower, which is approximately 735.5 watts (~736 watts).
While watts and kilowatts often describe both input and output power, HP is commonly used only for output power. In electrical devices, one HP is commonly 746 watts, although when checking European motors and similar devices, one may find one HP as being calculated as 736 watts.
- Amps (A) describes current strength,
- Amp Hours (Ah) describes the capacity of the batteries and is usually measured during the period of 20h,
- Volts (V) describes the operating voltage of a certain device, like motor, battery, generator and similar. For example, nominal voltage of US mains power is 110/120 volts, EU mains power is 220/230 volts, 6-cells lead-acid batteries (flooded, AGM, Gel Cells) is 12 volts etc.
Watts to Amps and Amps to Watts Formula
If you want to find watts from volts and amps (or vice versa), use the following formula:
P(W) = U(V) * I(A)
Power (measurement unit are watts (W)) = Voltage (measurement unit are volts (V)) * Current (measurement unit are Amps (A))
Similarly:
U(V) = P(W) / I(A)
I(A) = P(W) / U(A)
Note: power of DC (Direct Current) electrical devices is expressed in watts (W) or volt-amps (VA) which is (generally) the same. When calculating the power of AC (Alternate Current) motors and similar devices, one must take into account impedance/capacitance of such unit/electric cicruit by calculating cos(θ), where 'θ ' is 'angle' (phase shift) between the current and the voltage - when there is no phase shift:
cos(θ) = cos (0°) = 1
This happens most of the time in DC circuits, except when starting/stopping large(r) motors and similar loads. For short, in this article, we will assume that voltage and currents are in phase and that phase shift is zero!
So, if you want to convert volt-amps (VA) of DC circuit into the watts (W), than simply:
1 VA = 1 W
If you want to convert volt-amps of AC circuit into the watts (so-called 'real power'), than you must know the phase shift and use cosine:
1 W = 1 VA cos (θ)
Similarly, if you want to calculate so-called 'reactive power', than you must know the phase shift and use sine function:
1 W = 1 VA sin (θ)
Again, we will assume that there is no phase shift and that apparent and real power are the same and that reactive power is zero!
Watts to Amps and Amps to Watts Examples
When converting watts to amps and amps to watts, one must know the voltage of the electric load.
Example 1: Electric trolling motor draws 50 Amps from the 12 volts battery at full throttle - what is its power in watts?
P(W) = 12V * 50A = 600 W
Example 2: Electric trolling motor is rated at 2000 watts max and powered by three AGM batteries connected in series - what is its maximum current?
I(A) = 2000W / (3*12V) = ~55.55 Amps
Example 3: mains power (120V) electric water pump motor draws 3 Amps continuously, and 5 Amps when starting. Its power in watts are:
P_{cont}(W) = 120V * 3A = 360W
P_{max}(W) = 120V * 5A = 600W
Note: in this example, phase shift of this hypothetical motor is zero.
Watts to Amps Chart
The following Watts to Amps chart lists currents of specific loads, depending on the nominal voltage:
Power (Watts) | Power (HP) | Current @ Nominal Voltage | ||||
12 Volts | 24 Volts | 36 Volts | 120 Volts | 230 Volts | ||
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 |
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 values, we have used 1 HP = 746 watts.
As one can see in this Watts to Amps chart, the increase in power is followed by the increase of the required current. However, as the current goes up, so does the power losses in the wires. In order to keep the maximum current below acceptable 50-60 Amps, many motors and other units use higher voltages.
For example, small trolling motors (up to 55-60 pounds of thrust) are operated at 12 volts, while larger motors are powered by 24 or 36 volts.
Large industrial motors use 120/230 or more volts, and one or three phases to keep maximum currents as low as possible, while keeping the energy losses to acceptable levels.
Motor Horsepower (HP) to Amps
In many cases, people want to know the current of their motors, depending on the motor power stated in HPs. Those values may be read from the previous table, but they are also listed here, for more convenience:
1 HP Motor Amps: 62.16 Amps @12V; 31.08 Amps @24V; 20.72 Amps @36V; 6.216 Amps @120V; 3.243 Amps @230V,
2 HP Motor Amps: 124.3 Amps @12V; 62.16 Amps @24V; 41.44 Amps @36V; 12.43 Amps @120V; 6.487 Amps @230V,
3 HP Motor Amps: 186.5 Amps @12V; 93.25 Amps @24V; 62.16 Amps @36V; 18.65 Amps @120V; 9.730 Amps @230V,
4 HP Motor Amps: 248.6 Amps @12V; 124.3 Amps @24V; 82.88 Amps @36V; 24.86 Amps @120V; 12.97 Amps @230V,
5 HP Motor Amps: 310.8 Amps @12V; 155.4 Amps @24V; 103.6 Amps @36V; 31.08 Amps @120V; 16.21 Amps @230V.
Note: as said before, HPs is commonly used to describe/measure the output power of the motor - in that case one also has to calculate the energy/power loses in the motor.
For example: an electric motor with 90% efficiency coefficient (Co, sometimes CoP), 5 HP output power, with nominal voltage of 36 volts requires:
I(A)= (P(W) / U(V)) / Co = (3730 W / 36 V) / 0.90 = ~115.1 Amps
While ideal, 5 HP electric motor powered by 36 volts require 103.6 Amps, real life 5 HP electric motor requires ~115.1 Amps.
Keep this in mind when doing your math ...
Amps to Watts Chart
The following Amps to Watts chart lists power levels, depending on the specific current and nominal voltage:
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 |
As the current is increased, so is the power output - but, like said before, too large currents may increase energy losses beyond acceptable levels (and beyond the cooling system, if present, capabilities).
Thus, as the power requirements are increased, increase in nominal voltage keep the currents at acceptable levels.
Amp Hours (Ah) to Watts and Watts to Amp Hours (Ah) Formulas
This one is not as simple as watts to amps and amps to watts formulas.
While conversion from watts to amps and amps to watts is straightforward, one must note that Amp Hours (Ah) describe the capacity of the battery, while Watts (W) describe the power that is, for example, battery able to provide.
Because of that, batteries of the different capacities may provide the same power at the same time.
But (this is important), NOT for the same length of time.
While wrong assumptions may cause many problems, accurate assumptions may help significantly, including converting Amp Hours (battery capacity) to Watts and vice versa.
So, if we assume that the battery's voltage is fairly constant and that we know the battery's actual capacity, then the Amp Hours (Ah) to Watts (W)formula is:
P(W) = U(V) * I(A) = U(V) * (Actual Battery Amp Hours / T(h))
where T(h) is time (given in hours) during which the battery is being discharged.
While nominal capacity is given for the period of 20h, most battery manufacturers provide actual battery capacity for different discharging times (charging/discharging charts/graphs).
For example, UPG UB121000 Deep Cycle AGM Battery nominal (20h) capacity is 100 Ah, but the capacity drops as the discharging current is increased (typically for all lead-acid batteries):
- 20h discharge: 5 Amps, 100 Ah -> P = 12V * 5 Amps = ~60 W
- 10h discharge: 9.3 Amps, 93 Ah -> P= 12V * 9.3 Amps = ~111.6 W
- 5h discharge: 17 Amps, 85 Ah -> P= 12V * 17 Amps = ~204 W
- 1h discharge: 60 Amps, 60 Ah -> P= 12V * 60 Amos = ~720 W
Again: we have assumed that the voltage is constant (12V), but it is not - difference is not large, but it may be important in certain applications.
Similarly, Watts (W) to Amp Hours formula is:
Actual Battery Amp Hours = (P(W) * T(h)) / U(V)
In the case of UPG UB121000 Deep Cycle AGM Battery, this means that, for example, 10h capacity (Amp Hours) is:
Actual Battery Amp Hours = (111.6 W * 10) / 12V = 93 Ah
Again, the less assumptions one make, the more accurate calculation will be - just don't forget that one wrong assumption may ruin everything ...
When comparing two or more batteries, the best thing one can do is to compare the batteries of the same chemistry, voltage, and nominal capacity.
For example, one may compare 12V AGM 100 Ah batteries - very common batteries used for automotive, marine, industrial, off-the-grid and similar applications.
Note: Amazon affiliate links in the table open in the new windows, feel free to check them for most up-to-date offers and prices.
Now, let's compare two batteries, for example, Odyssey 31M-PC2150 and VMAXTANKS MR137-120.
Odyssey 31M-PC2150:
- dual purpose AGM battery,
- 100 Ah nominal capacity -> on average ~5 Amps for 20h, on average 60W for 20h,
- 205 minutes Reserve Capacity (RC) -> 25 Amps for 205 minutes, on average ~300W for 205 minutes,
- 1370 MCA -> it is able to provide 1370 Amps (at 32°F - 0°C) for 30 seconds, with the voltage not dropping below 7.2 V. At the cut-off voltage (7.2V), output power is 9864 watts.
VMAXTANKS MR137-120:
- deep cycle AGM battery,
- 120 Ah nominal capacity -> on average ~6 Amps for 20h, on average 72W for 20h,
- 230 minutes Reserve Capacity (RC) -> 25 Amps for 230 minutes, on average ~300W for 230 minutes,
- 900 MCA -> it is able to provide 900 Amps (at 32°F - 0°C) for 30 seconds, with the voltage not dropping below 7.2 V. At the cut-off voltage (7.2V), output power is 6480 watts.
As one can see, dual purpose Odyssey 31M-PC2150 is a clear winner regarding strong power output, but as the power output is decreased, deep cycle VMAXTANKS MR137-120 features prevail - although it is somewhat lighter battery, VMAXTANKS MR137-120 features better Reserve Capacity and nominal capacity values.
Long Story Short: when calculating Watts to Amps, Amps to Watts, Amp Hours (Ah) to Watts, Watts to Amp Hours (Ah) etc. be sure to know if and when assumptions are made as they can help in certain situations, but also oversimplification may cause results to deviate too much from real life values.
P.S. sorry about the math ...
:)