Kp calculator
Get the pressure equilibrium constant straight from partial pressures: for 2SO2 + O2 ⇌ 2SO3 with 0.4 atm of SO3, 0.2 atm of SO2 and 0.1 atm of O2, Kp comes out at 40, in atm to the power of −1. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
The pressure equilibrium constant Kp is the gas-phase mass-action expression written with partial pressures instead of molar concentrations. This Kp calculator takes the equilibrium partial pressures of every gaseous product and reactant together with their stoichiometric coefficients and returns Kp as the product of product pressures raised to their powers divided by the product of reactant pressures raised to theirs. You stay in one pressure unit across the list — atm, bar, or torr — because the numeric value of Kp carries that unit to the power of the gas-phase mole change.
What Kp means and how to read the result
The pressure equilibrium constant Kp is the equilibrium constant written with partial pressures of gases rather than with molarities. For a balanced reaction aA(g) plus bB(g) yields cC(g) plus dD(g) the mass-action law at equilibrium is Kp equals the product of product pressures each raised to its stoichiometric power, divided by the product of reactant pressures each raised to its power. Pure solids and liquids do not appear in the expression; only gas-phase species contribute.
Each stoichiometric coefficient is the exponent of that species equilibrium partial pressure, so doubling a coefficient squares that pressure in the product. Because every pressure must share one unit, Kp itself carries the unit of pressure raised to delta n, where delta n is the change in moles of gas — the sum of product coefficients minus the sum of reactant coefficients. This calculator does not convert atmospheres to bar or torr; you pick the unit and keep it for every species.
There is no computer-algebra approximation, no sampling of pressures, and no hidden temperature dependence: temperature is already baked into the equilibrium pressures you measured or were given. If you need Kc from concentrations, a conversion between Kp and Kc, or an unknown pressure from a known Kp, those are other tools.
Input contract, validation, and negative pressures
An optional name, species, formula, or label is echoed when present so result tables stay readable next to the numbers. Coefficients must be strictly positive: they are the exponents in Kp, not signed stoichiometric numbers that mix products and reactants in one list. A negative partial pressure is always rejected — a gas cannot have a negative pressure, and a silent absolute value would hide a data-entry bug as a plausible constant.
A product at zero pressure is allowed and yields Kp equal to zero, which is a finite, physically meaningful result when products are absent at equilibrium. Non-finite numbers, missing fields, empty strings, and arrays longer than thirty-two species per side are rejected with a message that names the field. Successful responses round numeric fields to twelve decimal places, collapse negative zero to zero, and omit unused optional keys such as a missing name.
Where a Kp calculator earns its keep
Students meet Kp when a gas-equilibrium chapter leaves concentration-based Kc and asks for the constant from a table of equilibrium partial pressures. Teachers can generate answer keys for Haber synthesis, sulfur dioxide oxidation, and phosphorus pentachloride dissociation drills without trusting a handheld calculator that silently switches units mid-problem. Lab notebooks that already list partial pressures from manometer, barometer, or gas-chromatography data can turn those numbers into Kp without re-deriving a full ICE table from initial moles.
Tutoring software and learning-management plugins call the same contract to mark a numeric Kp against a gold value with a tight tolerance. Process-education demos show Kp, the numerator, the denominator, and the gas-phase mole change so a learner can see the fraction, not only the final number. Pair it with a Kp-to-Kc converter when you have concentrations and temperature, with a Gibbs-to-K tool when you start from standard free energy, and with Dalton helpers when you only have mole fractions and total pressure.
Keep every pressure in one unit, pin the rounded kp in tests, and you get a reproducible gas-equilibrium constant without standing up a thermodynamics stack of your own.
What you can do with it
Homework and gas-equilibrium drills
Compute Kp from textbook equilibrium partial pressures and stoichiometric coefficients for Haber, SO2 oxidation, and PCl5 dissociation problems.
Lab notebooks and tutoring software
Turn measured product and reactant partial pressures into Kp for lab write-ups, plotters, and interactive lessons without a CAS kernel.
FAQ
What does the Kp calculator cost?
It is free in your browser on this page.
How is Kp defined here?
Kp is the product of each gaseous product partial pressure raised to its stoichiometric coefficient, divided by the product of each gaseous reactant partial pressure raised to its coefficient.
What happens if a partial pressure is negative?
A gas cannot have a negative partial pressure, so Kp is not computed.
What if a reactant partial pressure is zero?
A zero reactant pressure makes the denominator zero, so Kp is undefined.
Do all partial pressures need the same unit?
Yes. Keep atm, bar, torr, or any other pressure unit consistent across products and reactants. This calculator does not convert units; Kp then carries (pressure) to the power of delta n.
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/kp \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"products":[{"name":"SO3","partial_pressure":0.4,"coefficient":2}],"reactants":[{"name":"SO2","partial_pressure":0.2,"coefficient":2},{"name":"O2","partial_pressure":0.1,"coefficient":1}]}'const res = await fetch("https://api.kit.forhosting.com/chem/kp", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"products": [
{
"name": "SO3",
"partial_pressure": 0.4,
"coefficient": 2
}
],
"reactants": [
{
"name": "SO2",
"partial_pressure": 0.2,
"coefficient": 2
},
{
"name": "O2",
"partial_pressure": 0.1,
"coefficient": 1
}
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/kp",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"products": [
{
"name": "SO3",
"partial_pressure": 0.4,
"coefficient": 2
}
],
"reactants": [
{
"name": "SO2",
"partial_pressure": 0.2,
"coefficient": 2
},
{
"name": "O2",
"partial_pressure": 0.1,
"coefficient": 1
}
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/kp", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"products":[{"name":"SO3","partial_pressure":0.4,"coefficient":2}],"reactants":[{"name":"SO2","partial_pressure":0.2,"coefficient":2},{"name":"O2","partial_pressure":0.1,"coefficient":1}]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"products":[{"name":"SO3","partial_pressure":0.4,"coefficient":2}],"reactants":[{"name":"SO2","partial_pressure":0.2,"coefficient":2},{"name":"O2","partial_pressure":0.1,"coefficient":1}]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/kp", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"products": [
{
"name": "SO3",
"partial_pressure": 0.4,
"coefficient": 2
}
],
"reactants": [
{
"name": "SO2",
"partial_pressure": 0.2,
"coefficient": 2
},
{
"name": "O2",
"partial_pressure": 0.1,
"coefficient": 1
}
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.kp",
"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.
Limits
max_abs_value | 1000000000000000 |
max_species | 32 |
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
Negative partial pressures are rejected with invalid_input rather than producing a physically meaningless constant. Successful API calls cost $0.002; validation failures are not billed.
What Kp means and what the response contains
The response returns the numeric kp, the numerator and denominator of the mass-action quotient, delta_n, the normalized product and reactant rows, a species count, a method tag, and a compact formula string.
Input contract, validation, and negative pressures
Send a JSON body with two required arrays: products and reactants. Each entry is an object with a finite partial_pressure — aliases pressure, p, and P — and a positive stoichiometric coefficient — aliases coeff, nu, stoich, and n. Both arrays must be non-empty; an empty product list or empty reactant list is invalid_input because Kp is a quotient of two mass-action products. A reactant whose partial pressure is zero makes the denominator zero, so Kp is undefined and the request fails with invalid_input. The path never calls the network, never reads the clock, and never draws a random sample, so the same body always produces the same JSON. The free browser run on this page and a successful API request at $0.002 share that identical module.
Where a Kp calculator earns its keep
Because this is a tier-A parse capability, the work runs entirely in the browser on this page; through the API each successful evaluation costs $0.002 and failed validation is not charged.
Integration use cases
Deterministic test fixtures
Generate reproducible kp, numerator, denominator, and delta_n fields for unit tests, property checks, and CI assertions on gas equilibria.