Input power required calculator
A motor that must deliver 750 W at 85% efficiency needs an input of 882.352941176 W. Enter the useful output power and the efficiency as a fraction to get the required input, the efficiency as a percentage and the power lost. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Output power
- 750
- Efficiency
- 0.85
- Efficiency percent
- 85
- Input power
- 882.352941176
- Power loss
- 132.352941176
Every real machine wastes some of the power it draws: motors heat their windings, pumps dissipate fluid friction, and gearboxes lose energy in tooth mesh and bearings. When you only know the useful output power you need and a single overall efficiency figure, the required electrical or shaft input follows from one ratio. Input power required is defined as P_in equals P_out divided by η, where P_out is the useful mechanical or process power and η is the dimensionless efficiency between zero and one. This calculator accepts those two numbers, rejects a zero efficiency that would divide by zero, and returns the input power, the efficiency as a percent for display, and the power loss under the constant-efficiency model.
What input power required means and the defining formula
Efficiency for a steady machine is the ratio of useful power delivered to the power supplied at the input terminal or shaft: η equals P_out over P_in. Rearranging for the unknown supply gives the sizing formula this tool implements: P_in equals P_out divided by η. If a motor must deliver seven hundred fifty watts of mechanical power at eighty-five percent efficiency, the electrical input must be seven hundred fifty divided by zero point eight five, about eight hundred eighty-two watts.
Efficiency is expected as a fraction, not a percent: use zero point nine for ninety percent, not ninety. Negative efficiency is allowed mathematically if a client needs a signed model, but everyday machine sizing uses a positive fraction less than or equal to one.
Where input-power sizing shows up in real work
Secondary-school and college mechanics courses assign motor and machine problems that give useful power and efficiency and ask for the electrical or shaft input, often before students meet variable-efficiency maps or part-load curves. Plant and facility engineers size feeders, VFDs, and gensets by backing out required input from process power and a catalog overall efficiency so cable and protection selections stay conservative.
Pump and fan selection worksheets convert hydraulic or aerodynamic useful power into brake and then electrical power with staged efficiencies; a single overall η still gives a first-cut electrical load for early design. Curriculum authors and LMS plugins need a deterministic oracle that rejects zero efficiency instead of silently emitting Infinity that a buggy grader might accept. Failed validation does not consume balance.
Keep requests small, pin the cleaned numeric fields in tests, and you get reproducible input-power figures for homework, design notebooks, and edge workers without standing up a full machine-simulation stack of your own.
What you can do with it
Motor and machine homework checks
Given useful output power and overall efficiency, compute required electrical or shaft input so students and auto-graders share one ground truth.
Plant feeder and drive first-cut sizing
Back out input kilowatts from process power and a catalog efficiency before selecting cables, VFDs, or standby generators.
Exam keys and notebook scripts
Generate deterministic P_in answers for bulk problem sets, rejecting zero efficiency as invalid instead of Infinity.
FAQ
What happens if efficiency is zero?
Input power is undefined when η = 0 because the defining ratio would divide by zero.
Should I enter efficiency as a percent or a fraction?
As a fraction: use 0.9 for 90%, not 90. Passing 90 by mistake would understate the required input power.
Which power units can I use?
Any coherent power unit (W, kW, hp, etc.) as long as you treat output and input in the same unit. The ratio η is dimensionless.
How much power is lost as heat?
The difference between input and output. For 750 W of useful output at an efficiency of 0.85, the machine loses 132.352941176 W to heat, noise and other losses, assuming the efficiency stays constant.
Can I use it for a chain of motor, gearbox and pump?
Yes, as a first estimate: enter the useful power at the end of the chain and one overall efficiency for the whole set. The calculator does not model part-load curves or separate stages.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/mech/input-power-required \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"output_power":750,"efficiency":0.85}'const res = await fetch("https://api.kit.forhosting.com/mech/input-power-required", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"output_power": 750,
"efficiency": 0.85
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/input-power-required",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"output_power": 750,
"efficiency": 0.85
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/input-power-required", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"output_power":750,"efficiency":0.85}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"output_power":750,"efficiency":0.85}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/input-power-required", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"output_power": 750,
"efficiency": 0.85
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.input_power_required",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
What input power required means and the defining formula
The complementary quantity P_in minus P_out is the power converted to heat, noise, or other non-useful forms under the constant-efficiency idealization; the calculator returns that power_loss alongside the required input so energy balances and cooling checks stay in one response. Passing ninety by mistake would understate the input power by two orders of magnitude, so nameplate or catalog percent values must be divided by one hundred before the call. Zero efficiency is physically the limit of no conversion at all; the defining ratio would require infinite input for any non-zero output, so the API rejects η equals zero with invalid_input instead of returning Infinity.
Input contract, response shape, and error behaviour
When the absolute value of efficiency is below a tiny epsilon, the error message states that efficiency is zero and that input power cannot be computed because division by zero would occur in P_in equals P_out over η, so clients can correct the efficiency source rather than guessing. Classic checks include seven hundred fifty watts out at zero point eight five for about eight hundred eighty-two watts in; one thousand watts out at one hundred percent efficiency for one thousand watts in with zero loss; and a deliberate zero efficiency that must fail validation. Keep power units consistent so the ratio is dimensionless. Wire the free browser form for class demos and quick sizing, then call the same contract from scripts for bulk motor lists or exam answer keys. POST a JSON body with two required finite numbers: output_power, the target useful power P_out in watts or any coherent power unit you prefer, and efficiency, the dimensionless η such as zero point eight five for eighty-five percent. Aliases P_out, p_out, power_out, and useful_power map to output_power; eta, the Greek letter η, and eff map to efficiency. Missing fields, empty strings, NaN, and Infinity fail with invalid_input naming the field and are not billed. On success the body echoes cleaned output_power and efficiency, efficiency_percent as η times one hundred for labels and charts, input_power as the required supply, power_loss as input_power minus output_power, the formula string P_in equals P_out over η, and method input_power_required. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Technical questions
What formula does this input power required calculator use?
P_in = P_out / η, where output_power is P_out and efficiency is the dimensionless fraction η (for example 0.85 for 85%). The response also includes efficiency_percent and power_loss = P_in − P_out.
What does the input power required calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.