ForHosting KIT · Finance & money

Profit at given output calculator

At 20 units sold for 40 each, revenue is 800 and cost is 500, so profit is 300. Enter your revenue and cost formulas and an output level to see profit, loss or break-even at that point. Free in your browser.

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Worked example

If you enter

Quantity: 20
Tr linear: 40
Tr quadratic: 0
Fixed cost: 100
Tc linear: 10
Tc quadratic: 0.5

You get

Total revenue: 800
Total cost: 500
Variable cost: 400
Profit: 300

A firm's accounting profit at a chosen output is total revenue minus total cost evaluated at that quantity. Intermediate microeconomics supplies those two sides as functions of Q: a linear or quadratic revenue polynomial, and the usual short-run quadratic cost polynomial with a non-negative fixed bill. This profit at a given output calculator accepts those coefficients and a non-negative quantity, then returns TR, TC, and π = TR − TC at that Q, together with variable cost and a profit, loss, or break-even status. It does not maximize profit and it does not take a derivative; it answers the prior question every homework set and plant plan asks first — if the firm produced this many units under these functions, how much would it earn or lose.

What profit at a given output is, and which functions it uses

Accounting profit at a given output is the difference between what the firm collects and what it spends when it produces that quantity. Intermediate microeconomics writes both sides as functions of output Q so the same formulas can be evaluated at every candidate run size instead of at a single pair of totals. Total revenue is a linear or quadratic polynomial: TR of Q equals a linear coefficient times Q plus a quadratic coefficient times Q squared.

When the firm is a price taker the quadratic term is zero and the linear coefficient is the market price, so revenue collapses to price times quantity. When inverse demand is linear and downward sloping, price itself falls with Q and the quadratic coefficient is negative, which is the usual monopoly or imperfect-competition revenue function in problem sets. Total cost is the short-run quadratic used throughout the same textbooks: TC of Q equals a non-negative fixed cost plus a linear variable-cost term plus a quadratic variable-cost term.

Profit is defined pointwise as pi of Q equals TR of Q minus TC of Q. This calculator evaluates that identity at the Q you supply. It does not search for a profit-maximizing output, it does not set marginal revenue equal to marginal cost, and it does not take a derivative of the profit function.

Those are different questions with different search intent. Fixed cost is subtracted in full at every output, including zero, which is why producing nothing still leaves a loss equal to the fixed bill whenever fixed cost is positive. Variable cost is total cost minus fixed cost and is reported so you can rebuild the original TC polynomial from the response without re-entering the coefficients.

Where a profit-at-given-output calculator earns its keep

Introductory and intermediate microeconomics courses assign this exact move — write TR and TC as polynomials, pick a listed Q, subtract — because it is the first step toward the shutdown rule and toward comparing two candidate run sizes before anyone differentiates. Tutoring platforms and LMS plugins need a deterministic oracle that rejects negative output instead of silently returning a profit figure a buggy grader might accept.

Analysts who already have a fitted revenue curve and a fitted quadratic cost curve want the same closed-form profit at a planned run size without reopening a spreadsheet and risking a cell that adds tax or freight twice. This landing is not a profit-margin calculator: margin is a ratio from a single price and a single unit cost, whereas profit at a given output is a level from whole functions of Q.

Pin the rounded profit in tests, keep quantity and fixed cost non-negative, and you get reproducible TR, TC, and pi figures for homework, exam generators, and lightweight planning notebooks without standing up a computer-algebra system. Pair this capability with a marginal-cost-from-cost-function tool when you later need the slope of TC; keep this surface focused on evaluating profit at the output you already chose.

What you can do with it

Homework profit at a listed Q

Students enter TR and TC coefficients plus Q from a problem set and verify π = TR − TC against the textbook table of totals.

Plant run-size evaluation

Turn fitted quadratic revenue and cost functions into accounting profit at a planned output without approximating from a discrete table.

FAQ

How do you compute a firm's profit at a given output?

Evaluate the supplied functions at that Q and subtract: π(Q) = TR(Q) − TC(Q). This calculator uses TR(Q) = αQ + βQ² and TC(Q) = F + vQ + cQ².

How is this different from a profit-margin calculator?

Profit margin is a ratio from one price and one unit cost. Profit at a given output is a currency level from whole revenue and cost functions of Q.

What revenue and cost functions does the calculator accept?

Quadratic TR(Q) = αQ + βQ² (set β = 0 for a competitive firm so TR = P·Q) and quadratic TC(Q) = F + vQ + cQ² with non-negative fixed cost F.

Does this find the profit-maximizing output?

No. It evaluates profit at the Q you already chose. It does not set MR = MC or search over quantities.

Why is there a loss when output is zero?

Because the fixed cost is subtracted in full at every output, including zero. With a fixed cost of 100, producing nothing still leaves a loss of 100, even though revenue and variable cost are both zero.

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

POSThttps://api.kit.forhosting.com/econ/profit-at-output

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/econ/profit-at-output \
  -H "Authorization: Bearer $KIT_KEY" \
  -H "Content-Type: application/json" \
  -d '{"quantity":20,"tr_linear":40,"tr_quadratic":0,"fixed_cost":100,"tc_linear":10,"tc_quadratic":0.5}'

const res = await fetch("https://api.kit.forhosting.com/econ/profit-at-output", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.KIT_KEY}`,
    "Content-Type": "application/json"
  },
  body: JSON.stringify({
    "quantity": 20,
    "tr_linear": 40,
    "tr_quadratic": 0,
    "fixed_cost": 100,
    "tc_linear": 10,
    "tc_quadratic": 0.5
  })
});
const { task_id } = await res.json();

import os, requests

res = requests.post(
    "https://api.kit.forhosting.com/econ/profit-at-output",
    headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
    json={
    "quantity": 20,
    "tr_linear": 40,
    "tr_quadratic": 0,
    "fixed_cost": 100,
    "tc_linear": 10,
    "tc_quadratic": 0.5
},
)
task_id = res.json()["task_id"]

<?php
$res = file_get_contents("https://api.kit.forhosting.com/econ/profit-at-output", false, stream_context_create([
  "http" => [
    "method"  => "POST",
    "header"  => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
    "content" => '{"quantity":20,"tr_linear":40,"tr_quadratic":0,"fixed_cost":100,"tc_linear":10,"tc_quadratic":0.5}',
  ],
]));
$task = json_decode($res, true);

body := bytes.NewBufferString(`{"quantity":20,"tr_linear":40,"tr_quadratic":0,"fixed_cost":100,"tc_linear":10,"tc_quadratic":0.5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/econ/profit-at-output", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)

Example request

{
  "quantity": 20,
  "tr_linear": 40,
  "tr_quadratic": 0,
  "fixed_cost": 100,
  "tc_linear": 10,
  "tc_quadratic": 0.5
}

Example response

{
  "task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
  "type": "econ.profit_at_output",
  "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

Per request$0.002

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

Inputs, the closed-form subtraction, outputs, and validation

The field quantity is the output Q at which you want profit; it must be non-negative — output cannot be negative — and zero is allowed because a firm that produces nothing still owes its fixed bill. Display strings rewrite TR, TC, and pi with the numeric coefficients, and formula restates the identity pi of Q equals TR of Q minus TC of Q. Example: price forty, competitive beta zero, fixed cost one hundred, v ten, c one half, Q twenty yields TR of eight hundred, TC of five hundred, and profit of three hundred. POST a JSON body with six required finite numbers. The field tr_linear is the coefficient alpha of Q in TR of Q equals alpha Q plus beta Q squared; for a competitive firm this is simply the market price. The field tr_quadratic is the coefficient beta of Q squared; set it to zero for a price taker, or to a negative number when inverse demand is linear. The field fixed_cost is the constant F in the cost function and must be non-negative. The fields tc_linear and tc_quadratic are the remaining cost coefficients v and c. Textbook aliases such as q, price, p, fc, and beta are accepted. On success the response echoes the six inputs, returns total_revenue, total_cost, variable_cost, and profit, labels the sign with profit_status as profit, loss, or break_even, and, when Q is positive, also returns average_revenue, average_cost, and profit_per_unit. Missing, empty, or non-finite fields fail naming the field; a negative quantity or a negative fixed cost fails with invalid_input. Failed validation is not billed; successful parse calls use the published $0.002 base price.

Integration use cases

LMS and tutoring auto-grading

Score “find profit at Q from these revenue and cost functions” items with a deterministic oracle that rejects negative output as invalid_input.

Technical questions

What does the profit at given output calculator cost?

The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.

Read the full KIT documentation →

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