Atom economy calculator
Measure how much of the reactants ends up in the product: hydrating ethene to ethanol, 46.07 g/mol on both sides, scores 100 %. Give the two molar masses and get the atom economy and its waste share. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Product molar mass
- 88.11
- Reactant molar mass
- 106.12
- Atom economy fraction
- 0.8302864681
- Atom economy percent
- 83.0286468149
- Waste fraction
- 0.1697135319
- Waste percent
- 16.9713531851
Atom economy is the green-chemistry metric that asks what fraction of reactant atoms end up in the desired product rather than in by-products or stoichiometric waste. Barry Trost formalized the idea so that synthetic routes can be ranked by how completely they incorporate starting-material mass into the target, independent of experimental yield. The closed form is simple: divide the molar mass of the desired product by the total molar mass of all reactants as written in the balanced equation, then multiply by one hundred for a percentage. This calculator accepts those two molar masses, returns atom economy as a fraction and as a percent, and also reports the complementary waste fraction so lab reports and process reviews can cite both numbers without a second tool.
How atom economy measures green reaction design
Start from a balanced chemical equation written so that the coefficient of the desired product is one, or scale both sides consistently so product and reactant totals stay in the same basis. Sum the molar masses of every reactant species multiplied by their stoichiometric coefficients; that sum is the total reactant molar mass.
Divide the molar mass of the single desired product formula unit by that sum to obtain the atom-economy fraction between zero and one when product mass does not exceed reactant mass, then multiply by one hundred for the familiar percentage. One hundred percent means every reactant atom is incorporated into the product in the idealized stoichiometry; lower values flag intentional co-products such as water, salts, or leaving groups that leave the reaction as waste even if isolation is perfect.
Atom economy is therefore complementary to percent yield: yield asks how much product you isolated relative to theoretical maximum, while atom economy asks how wasteful the balanced equation itself is even at one hundred percent yield. Negative product molar mass is rejected for the same reason.
Where atom economy calculators show up in real work
Secondary-school and introductory university green chemistry modules assign atom-economy drills that compare addition reactions at one hundred percent with substitution or elimination routes that leave stoichiometric by-products; a single trusted oracle speeds grading and demo setup without hand-waving floating-point noise. Organic synthesis courses rank candidate routes to the same target by atom economy before lab time is spent measuring yield, so students learn that high yield on a low-economy equation still generates large co-product waste.
Process chemists and sustainability teams screen early-stage routes when only balanced equations and formula weights are known, before solvent and catalyst metrics enter the full process mass intensity calculation. If you later need percent yield from actual and theoretical product masses, limiting-reagent leftovers, E-factor from waste mass, or automatic molar-mass lookup from a chemical formula, treat those as separate search intents and landings rather than overloading this atom economy calculator page.
What you can do with it
Homework and green-chemistry answer keys
Compute AE% = (M_product / M_reactants) × 100 from balanced-equation molar masses so students and auto-graders share one closed-form ground truth.
Route screening before lab work
Rank candidate synthetic routes by atom economy using only product and total reactant formula weights, before measuring experimental yield.
FAQ
What is atom economy?
Atom economy is the percentage of reactant atoms (by mass) that end up in the desired product: AE% = (M_product / M_reactants) × 100 using molar masses from the balanced equation.
Is atom economy the same as percent yield?
No. Percent yield compares actual isolated product to theoretical maximum. Atom economy rates the balanced equation itself: even 100% yield can leave large stoichiometric waste if AE is low.
What does it cost?
The browser tool is free and runs locally.
How do I calculate atom economy for a reaction?
Balance the equation, add the molar masses of all reactants multiplied by their coefficients, and divide the molar mass of the desired product by that sum. Multiply by 100 for the percentage.
What does a low atom economy tell me?
That the balanced equation itself throws atoms away as co-products such as water, salts or leaving groups. Even with perfect isolation that mass ends up as waste, which the tool reports as the waste percentage.
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/chem/atom-economy \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"product_molar_mass":88.11,"reactant_molar_mass":106.12}'const res = await fetch("https://api.kit.forhosting.com/chem/atom-economy", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"product_molar_mass": 88.11,
"reactant_molar_mass": 106.12
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/atom-economy",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"product_molar_mass": 88.11,
"reactant_molar_mass": 106.12
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/atom-economy", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"product_molar_mass":88.11,"reactant_molar_mass":106.12}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"product_molar_mass":88.11,"reactant_molar_mass":106.12}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/atom-economy", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"product_molar_mass": 88.11,
"reactant_molar_mass": 106.12
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.atom_economy",
"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
Zero total reactant mass is rejected with a clear invalid_input error because the quotient is undefined. No network, no random seeds, and no wall-clock timestamps: identical inputs always produce identical JSON.
How atom economy measures green reaction design
Zero or negative total reactant molar mass makes the quotient undefined or non-physical, so those cases fail validation with a clear invalid_input message rather than Infinity or a silent NaN. This capability evaluates the closed form in deterministic floating-point arithmetic: no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical inputs always produce identical JSON. It does not balance equations for you, look up formula weights from molecular formulas or SMILES, compute experimental percent yield from actual and theoretical masses, or report E-factor or process mass intensity; those are separate search intents with their own landings when product coverage grows.
What you send and what you get back
Classic textbook checks include ethyl acetate formation where product eighty-eight point one one and reactants one hundred six point one two give roughly eighty-three percent atom economy, and ethene hydration to ethanol where product and reactant totals both equal forty-six point zero seven for a perfect one hundred percent. Keep both masses on the same stoichiometric basis: if your equation produces two product formula units, either double the product molar mass or use the per-formula-unit equation so the ratio stays meaningful. Send two required finite numbers under the fields product_molar_mass and reactant_molar_mass. product_molar_mass is the molar mass of the desired product in grams per mole and must be greater than or equal to zero. reactant_molar_mass is the total molar mass of all reactants in grams per mole for the balanced equation and must be strictly greater than zero; zero or negative values fail with invalid_input because atom economy divides by total reactant mass. Missing fields, non-numeric strings, NaN, Infinity, negative product mass, and non-positive reactant mass fail with invalid_input and are not charged. On success the response echoes cleaned product_molar_mass and reactant_molar_mass, provides atom_economy_fraction and atom_economy_percent as primary results, includes waste_fraction and waste_percent as one minus the economy metrics, attaches a units hint object naming grams per mole and percent, sets method to atom_economy, and formula to AE percent equals M product over M reactants times one hundred so homework write-ups can cite the same expression. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where atom economy calculators show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Sustainability and process review notes
Document waste_percent alongside atom_economy_percent when writing green-chemistry justification sections for reports and design reviews.
Technical questions
What happens if reactant molar mass is zero?
The request fails with invalid_input. Atom economy divides by total reactant mass, so zero or negative reactant_molar_mass is rejected rather than returning Infinity or NaN.
How do I format the input?
Send product_molar_mass (desired product g/mol, ≥ 0) and reactant_molar_mass (sum of all reactant g/mol with coefficients, > 0). Both must be finite numbers.