Buffer capacity calculator
Measure how strongly a buffer resists pH change: 0.1 mol/L of weak acid and 0.1 mol/L of its conjugate base give a capacity of 0.11512925465 mol/(L·pH), the most that total can offer. Enter the two concentrations. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Acid
- 0.1
- Conjugate base
- 0.1
- Total concentration
- 0.2
- C
- 0.2
- Fraction acid
- 0.5
- Fraction base
- 0.5
A buffer capacity calculator turns the weak-acid and conjugate-base concentrations of a monoprotic buffer into the single number that measures how strongly the mixture resists pH change. Enter [HA] and [A−] in any consistent concentration unit; the tool returns β from the classroom Van Slyke form β equals the natural logarithm of ten times the product of the two concentrations divided by their sum, plus total concentration, mole fractions, the equimolar maximum β_max for that total, step-by-step substitution, and a short balance label. Homework checks, lab prep, titration planning, and coding kata expected values all need that same deterministic β without opening a spreadsheet.
What buffer capacity means for a monoprotic HA / A− pair
Buffer capacity, often written with the Greek letter beta, quantifies how much strong acid or strong base must be added to shift the pH of a buffer by one unit. For a monoprotic weak acid HA in equilibrium with its conjugate base A− under the usual dilute aqueous approximations, and when the self-ionization terms of water are neglected, the composition-dependent capacity collapses to a simple closed form: beta equals the natural logarithm of ten multiplied by the product of the two form concentrations and then divided by their sum.
The natural logarithm of ten is about 2.302585, which is why many textbooks write a factor of 2.303 in front of the same ratio. The sum C equals [HA] plus [A−] is the total analytical concentration of the buffer pair; it must be strictly positive because division by zero would make capacity undefined. When one form is present alone, the product in the numerator vanishes and capacity is zero—the mixture cannot neutralize both directions of pH attack.
Practical tips, limits, and related searches
Keep both concentrations non-negative and inside the published absolute range so the product and quotient cannot overflow into a non-finite capacity that the solver must reject. Prefer sending numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. Near-zero totals after floating noise are rejected as zero total so a blank buffer is not reported as a finite capacity.
Prefer this capability when you already have [HA] and [A−] and only need beta; if you need buffer pH from pKa and the ratio, use the related Henderson–Hasselbalch calculator instead.
What you can do with it
Homework checks for Van Slyke-style capacity
Students enter [HA] and [A−] from textbook buffer problems and compare hand-written β, total C, and equimolar β_max against a deterministic result before submitting.
Lab buffer prep and composition screening
Pick relative acid and salt amounts at a fixed total concentration and rank candidate recipes by predicted buffer capacity before mixing stock solutions.
FAQ
What formula does this buffer capacity calculator use?
β = ln(10) × ([HA] × [A−]) / ([HA] + [A−]), the common monoprotic form with water autoionization neglected. Textbooks often write the factor as 2.303.
What happens when total concentration is zero?
When [HA] + [A−] = 0 the capacity is undefined.
Does this need pKa or pH?
No. This composition form depends only on [HA] and [A−]. Use a Henderson–Hasselbalch calculator if you need buffer pH from pKa and the ratio.
Is the buffer capacity calculator free?
The browser tool is free and runs locally.
Which mix of acid and base gives the highest capacity?
Equal concentrations of both. For a given total concentration, capacity peaks when the two forms are equimolar, at about 0.576 times the total, which is why balanced buffers are the ones that resist pH change best.
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/buffer-capacity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"acid":0.1,"conjugate_base":0.1}'const res = await fetch("https://api.kit.forhosting.com/chem/buffer-capacity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"acid": 0.1,
"conjugate_base": 0.1
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/buffer-capacity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"acid": 0.1,
"conjugate_base": 0.1
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/buffer-capacity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"acid":0.1,"conjugate_base":0.1}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"acid":0.1,"conjugate_base":0.1}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/buffer-capacity", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"acid": 0.1,
"conjugate_base": 0.1
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.buffer_capacity",
"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 | 1000000000000 |
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
When the total concentration is zero the capacity is undefined, so the API returns a clear invalid_input error instead of inventing a zero.
What buffer capacity means for a monoprotic HA / A− pair
Capacity is largest for a given total C when the two forms are equimolar, which recovers the familiar maximum beta_max equals ln(10) times C over four, or roughly zero point five seven six times C. This calculator focuses on that composition formula only: it does not solve for pH from pKa, does not integrate a full speciation model, and does not add the free hydrogen and hydroxide contributions that matter in extremely dilute or extreme-pH systems. That separation keeps the SEO intent sharp: people searching for a buffer capacity calculator from acid and salt concentrations get a transparent arithmetic answer they can check by hand.
How to call the API and what comes back
Their sum—the total buffer concentration—must be strictly greater than zero; values whose absolute sum is at or below one times ten to the minus fifteen are treated as zero total and rejected. Send a JSON body with two required finite numbers: acid (aliases HA, acid_concentration, ha, weak_acid) and conjugate_base (aliases A_minus, base, base_concentration, a_minus, salt). Both must be non-negative and each absolute value must stay within the published limit of one trillion so intermediate products remain finite in IEEE double precision on the Worker and in the browser. On success the response echoes rounded acid and conjugate_base, sets total_concentration and C to the same rounded sum, fraction_acid and fraction_base to the mole fractions of each form, buffer_capacity together with the mirrors beta and capacity to the rounded beta value, beta_max to the equimolar maximum at that total C, ln10 to the rounded natural logarithm of ten used in the product, formula to the string beta equals ln of ten times product over sum, balance to one of balanced, acid_rich, base_rich, or single_form, unit_concentration to mol per litre, unit_capacity to mol per litre per pH unit, message to a short English summary, and steps to an ordered array of substitution lines. Failed validation—missing fields, non-finite numbers, negative concentrations, values outside absolute limits, or zero total concentration—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price.
Practical tips, limits, and related searches
When teaching, pair examples: equal tenth-molar acid and base yield the maximum beta for C equals zero point two; a ten-to-one imbalance lowers capacity at the same total; pure acid with zero conjugate base yields capacity zero while still accepting a nonzero total; and acid zero with conjugate base zero demonstrates the hard invalid_input path required by the contract. This landing targets people searching for a buffer capacity calculator, Van Slyke beta, or acid and conjugate base capacity online; it is not a Henderson–Hasselbalch pH tool, not a conjugate-ratio solver, and not a full aqueous speciation package. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately set both concentrations to zero. Round-trip checks are easy: recompute the natural logarithm of ten times the product of the two concentrations divided by their sum by hand and confirm it equals the published buffer_capacity within the same twelve-decimal rounding, and confirm that beta_max equals ln of ten times C over four for the published total.
Integration use cases
Unit tests for student buffer solvers
Generate known-good balanced and imbalanced capacity cases plus deliberate zero-total rejections for coding kata expected values.
Technical questions
Can one concentration be zero?
Yes. A pure acid or pure conjugate-base solution with nonzero total yields β = 0 (single_form). Only a zero total is rejected.