Fisher ideal price index
A Fisher index of 1.05 means prices rose 5 % overall, measured as the geometric mean of Laspeyres and Paasche so that neither the old nor the new basket decides alone. Enter prices and quantities for both periods. Free in your browser.
- Free
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Run — free
Worked example
- Prices base
- 10, 20, 5
- Prices current
- 12, 22, 6
- Quantities base
- 3, 2, 4
- Quantities current
- 2, 3, 5
- N
- 3
- Sum p0 q0
- 90
- Sum p1 q0
- 104
- Sum p0 q1
- 105
The Fisher ideal price index is the standard two-period index that reconciles the Laspeyres and Paasche formulas by taking their geometric mean. Economists, national accountants, and inflation analysts use it when a single number must summarize pure price change without locking the basket to only base-period or only current-period quantities. This Fisher ideal price index calculator accepts four equal-length series—base prices, current prices, base quantities, and current quantities—computes the Laspeyres index as the ratio of current prices valued at base quantities over base-period expenditure, computes the Paasche index with current quantities, and returns the Fisher index as the square root of their product. Intermediate basket sums and the percent change from a base of one are included so you can audit the arithmetic in a spreadsheet or exam solution.
What the Fisher ideal price index measures
A price index answers how much more (or less) a fixed notion of consumption costs in the current period relative to a base period. The Laspeyres price index holds quantities at base-period levels: it is the cost of buying the base basket at current prices divided by the cost of that same basket at base prices, written P_L equals sum of p1 times q0 over sum of p0 times q0.
Laspeyres tends to overstate inflation when consumers substitute away from goods that become relatively expensive, because it never updates the weights. The Paasche price index instead uses current-period quantities: P_P equals sum of p1 times q1 over sum of p0 times q1. Paasche tends to understate inflation for the symmetric reason—it values the basket people actually buy after substitution has already occurred.
Irving Fisher’s ideal index takes the geometric mean of the two, P_F equals the square root of P_L times P_P. That construction satisfies time-reversal (the index from period 1 back to period 0 is the reciprocal of the forward index) and factor-reversal properties that pure Laspeyres or pure Paasche lack. A Fisher value of one means no overall price change; 1.05 means a five percent rise; 0.97 means a three percent fall.
Where the Fisher index is most useful
National-account and CPI research sandboxes often prototype two-period comparisons before chaining multilateral methods—Fisher on a fixed commodity list is the textbook bridge between Laspeyres CPI series and superlative indexes. Corporate finance and procurement teams comparing unit prices across contract years with changing purchase volumes use Fisher when neither last year’s mix nor this year’s mix alone is a fair weight. Failed validation does not consume balance.
Keep series aligned by commodity order, document your base period clearly, and pin the rounded fisher field in tests so grading scripts and edge workers stay reproducible without standing up spreadsheet macros or R sessions for a four-array geometric mean.
What you can do with it
Two-period CPI and national accounts prototypes
Compute a superlative Fisher price comparison for a fixed commodity list before chaining longer time series.
Procurement and contract price reviews
Summarize pure price change when purchase volumes shift between base and current contract years.
FAQ
How is the Fisher ideal price index calculated?
Compute Laspeyres P_L = Σ(p1·q0)/Σ(p0·q0) and Paasche P_P = Σ(p1·q1)/Σ(p0·q1), then P_F = √(P_L·P_P).
What if the four arrays have different lengths?
All four series must describe the same ordered basket of items.
Why are negative prices or quantities rejected?
A classical price index assumes non-negative prices and quantities. Negative entries would break the interpretation of basket expenditure and can make the geometric mean non-real.
Why use Fisher instead of Laspeyres or Paasche?
Laspeyres keeps base-period quantities and tends to overstate inflation when people switch away from pricier goods; Paasche uses current quantities and tends to understate it. Fisher's geometric mean sits between them and passes the time-reversal test.
What does a Fisher index of 1.05 mean?
Prices rose five percent between the two periods. A value of 1 means no overall change, and 0.97 means a fall of three percent. The percent change is shown next to the ratio.
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/stat/fisher-price-index \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"prices_base":[10,20,5],"prices_current":[12,22,6],"quantities_base":[3,2,4],"quantities_current":[2,3,5]}'const res = await fetch("https://api.kit.forhosting.com/stat/fisher-price-index", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"prices_base": [
10,
20,
5
],
"prices_current": [
12,
22,
6
],
"quantities_base": [
3,
2,
4
],
"quantities_current": [
2,
3,
5
]
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/fisher-price-index",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"prices_base": [
10,
20,
5
],
"prices_current": [
12,
22,
6
],
"quantities_base": [
3,
2,
4
],
"quantities_current": [
2,
3,
5
]
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/fisher-price-index", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"prices_base":[10,20,5],"prices_current":[12,22,6],"quantities_base":[3,2,4],"quantities_current":[2,3,5]}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"prices_base":[10,20,5],"prices_current":[12,22,6],"quantities_base":[3,2,4],"quantities_current":[2,3,5]}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/fisher-price-index", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"prices_base": [
10,
20,
5
],
"prices_current": [
12,
22,
6
],
"quantities_base": [
3,
2,
4
],
"quantities_current": [
2,
3,
5
]
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.fisher_price_index",
"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
Length mismatches, empty baskets, negative values, and zero denominators fail with invalid_input instead of a silent NaN. The same pure module powers the free browser tool and the prepaid API path at $0.002 per successful call.
What the Fisher ideal price index measures
Reporting percent_change as one hundred times (P_F minus one) gives the familiar inflation-style percentage beside the pure ratio. This endpoint always returns both intermediate indices so you can see how much Laspeyres and Paasche diverge before the geometric mean is taken, which is useful in teaching and in quality checks on microdata.
Input contract, formulas, and error behaviour
Each entry must be a finite non-negative number; numeric strings that parse as finite decimals are accepted. Values are rounded to twelve decimal places for stable goldens across runtimes. Cap each series at ten thousand items; magnitudes beyond one times ten to the fifteen are rejected to keep floating products finite. POST a JSON body with four required arrays of equal length: prices_base (p0), prices_current (p1), quantities_base (q0), and quantities_current (q1). Empty arrays, length mismatches across the four series, negative prices or quantities, missing fields, and non-numeric tokens all fail with invalid_input and are not billed. If the Laspeyres denominator sum p0 times q0 is not strictly positive, or the Paasche denominator sum p0 times q1 is not strictly positive, the request fails with a clear message that the basket value is zero—typically because every base price or every paired quantity is zero. On success the body includes n (item count), the four rounded basket sums, laspeyres, paasche, fisher, percent_change from base one hundred scale, and a formula string restating P_F equals square root of P_L times P_P. Example with prices_base ten twenty five, prices_current twelve twenty-two six, quantities_base three two four, quantities_current two three five yields positive Fisher slightly above one when prices rose on every item.
Where a Fisher price index API earns its keep
Classroom and exam workflows need a deterministic oracle for homework that asks students to compute Laspeyres, Paasche, and Fisher by hand from a short table of prices and quantities; calling this endpoint after the student submits numbers catches arithmetic slips without a full statistical package. Content sites that rank for fisher ideal price index calculator benefit from a live free browser path whose results match the paid API byte-for-byte on the same pure module.
Integration use cases
Homework and exam checks
Verify student Laspeyres, Paasche, and Fisher answers from a short price–quantity table with a deterministic API oracle.
Technical questions
What does a Fisher index of 1.05 mean?
Prices rose about five percent relative to the base period on a superlative (geometric mean of Laspeyres and Paasche) measure. percent_change is 100×(fisher−1), so about 5.
What does the Fisher ideal price index calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.