Mixing three solutions calculator
100 mL at 2 M, 200 mL at 0.5 M and 50 mL at 1 M combine into 350 mL at exactly 1 M. Enter three concentrations and volumes of one solute and see how much each pour adds to the final mixture. Free in your browser.
- Free
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- No sign-up
- Your data stays on your device
Run — free
Worked example
- Concentration of solution 1
- 2
- Volume of solution 1
- 100
- Concentration of solution 2
- 0.5
- Volume of solution 2
- 200
- Concentration of solution 3
- 1
- Volume of solution 3
- 50
- Amount1
- 200
- Amount2
- 100
- Amount3
- 50
- Total solute
- 350
When three solutions of the same solute are poured into one vessel, the final concentration is the total amount of solute divided by the total volume, assuming ideal additive volumes and conservation of solute. For concentrations C1, C2, C3 and volumes V1, V2, V3 the closed form is C_f equals (C1 times V1 plus C2 times V2 plus C3 times V3) divided by (V1 plus V2 plus V3). This calculator accepts those six numbers in any consistent pair of units, returns every intermediate amount, the combined volume, and the final concentration, and rejects a zero total volume so empty mixtures are never presented as a defined concentration.
How mixing three solutions yields the final concentration
Start from three separate solutions that share one solute and the same concentration unit, for example molarity, grams per litre, or milligrams per millilitre. Label them with concentrations C1, C2, and C3 and volumes V1, V2, and V3 measured in one shared volume unit such as millilitres or litres. Under the ideal mixing assumption each portion contributes an amount of solute equal to concentration times volume, so amount one is C1 times V1, amount two is C2 times V2, and amount three is C3 times V3.
When the three portions are combined without chemical reaction and without volume contraction or expansion beyond simple addition, the total solute is the sum of the three amounts and the total volume is the sum of the three volumes. The final concentration is therefore total solute divided by total volume, which expands algebraically to the familiar weighted average C_f equals (C1 V1 plus C2 V2 plus C3 V3) over (V1 plus V2 plus V3).
If one volume is zero that solution contributes nothing and the formula reduces to a two-stream mix; if two volumes are zero the final concentration equals the remaining non-zero stream. If every volume is zero there is no mixture at all and division by zero is undefined, so the calculator rejects that case with invalid input rather than returning infinity or NaN. Entries must be finite; NaN and Infinity are rejected.
Negative concentrations and negative volumes fail early because they have no physical meaning in this mass-balance model. Concentrations and volumes may be zero individually as long as the summed volume stays positive.
What you send and what you get back
Send six required fields. The fields c1, c2, and c3 are the three concentrations as finite non-negative numbers in whatever unit your protocol uses; the output final concentration is expressed in that same unit. The fields v1, v2, and v3 are the three volumes as finite non-negative numbers in one shared volume unit.
Classic textbook checks include mixing two hundred millilitres of two molar solution with one hundred millilitres of half molar and fifty millilitres of one molar stock, and mixing equal volumes of three different concentrations to verify the arithmetic mean. Because the path is pure parse math, latency stays sub-millisecond for ordinary classroom and laboratory numbers.
Where three-solution mixing calculators show up in real work
Secondary-school and college general chemistry courses constantly assign mixture problems with two or three stocks of different molarity poured into one flask; a single trusted oracle that returns each amount beside the final concentration speeds grading and demo setup. Analytical labs combine working standards from three intermediate dilutions and need exact theoretical concentrations before they measure assay response. Process and formulation teams blend intermediate lots of the same active ingredient at different strengths and want a transparent weighted-average check before committing batch records.
Quality teams writing SOPs for multi-stream pooling document final concentration as a mass balance and need machine-readable results that match hand arithmetic on the same six inputs. If you later need serial dilution steps, water volume to add for a target concentration, or multi-solute ionic strength, treat those as separate search intents and landings rather than overloading this mixing three solutions calculator page.
What you can do with it
Homework and exam answer keys
Generate final concentration and per-stream solute amounts for textbook three-solution mixture sets so teachers and auto-graders share one ground truth.
Lab prep of pooled standards
Combine three intermediate stocks of known concentration and volume into one theoretical final concentration before assay.
FAQ
How is the final concentration calculated?
C_f = (C1·V1 + C2·V2 + C3·V3) / (V1 + V2 + V3), the total solute amount divided by the total volume under ideal additive mixing.
Can one of the volumes be zero?
Yes. A zero volume simply contributes no solute and no volume; the formula reduces to a two- or one-stream mix as long as the remaining total volume is positive.
What units should I use?
Any consistent pair: concentrations in one unit (e.g. M or g/L) and volumes in one unit (e.g. mL or L). The calculator does not convert units; final concentration matches the concentration unit you send.
What does it cost?
The browser tool is free and runs locally.
What do I get if I mix 100 mL at 2 M, 200 mL at 0.5 M and 50 mL at 1 M?
A final concentration of 1 M. The three portions carry 200, 100 and 50 units of solute, 350 in all, spread over 350 mL of total volume.
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/mixing-three-solutions \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"c1":2,"v1":100,"c2":0.5,"v2":200,"c3":1,"v3":50}'const res = await fetch("https://api.kit.forhosting.com/chem/mixing-three-solutions", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"c1": 2,
"v1": 100,
"c2": 0.5,
"v2": 200,
"c3": 1,
"v3": 50
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/mixing-three-solutions",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"c1": 2,
"v1": 100,
"c2": 0.5,
"v2": 200,
"c3": 1,
"v3": 50
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/mixing-three-solutions", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"c1":2,"v1":100,"c2":0.5,"v2":200,"c3":1,"v3":50}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"c1":2,"v1":100,"c2":0.5,"v2":200,"c3":1,"v3":50}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/mixing-three-solutions", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"c1": 2,
"v1": 100,
"c2": 0.5,
"v2": 200,
"c3": 1,
"v3": 50
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.mixing_three_solutions",
"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
How mixing three solutions yields the final concentration
The entire pipeline is 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.
What you send and what you get back
Missing fields, non-numeric strings, NaN, Infinity, negative concentrations, negative volumes, and a total volume of zero or numerically indistinguishable from zero fail with invalid_input and are not charged. On success the response echoes the cleaned concentrations and volumes, the per-solution solute amounts amount1 through amount3, total_solute, total_volume, final_concentration, and the formula and method labels for audit trails. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where three-solution mixing 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
SOP and QC fixtures
Bulk-produce weighted-average results for multi-stream pooling protocols and reject zero total volume with hard invalid_input.
Technical questions
What happens if total volume is zero?
The request fails with invalid_input. Final concentration is undefined when V1+V2+V3 = 0, so the calculator never returns Infinity or NaN.