Critical power two-point calculator
Two maximal efforts are enough: 300 seconds at 350 W and 1200 seconds at 300 W give a critical power of about 283.33 W and a W′ of 20 kJ. Use it as an educational estimate for cycling, rowing or running with power. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Duration 1
- 300
- Power 1
- 350
- Duration 2
- 1,200
- Power 2
- 300
- Work 1
- 105,000
- Work 2
- 360,000
- Critical power
- 283.333333333
- W prime
- 20,000
Critical power is the theoretical sustainable power ceiling used across cycling, running with power, and lab ergometry, while W′ (W-prime) is the finite anaerobic work capacity available above that ceiling. The classic two-point method needs only two truly maximal mean-power efforts at clearly different durations—typically something like a three-to-five-minute all-out and a twelve-to-twenty-minute all-out—then solves the linear work-versus-time relation for the slope (critical power) and intercept (W′). This critical power two-point calculator applies that exact deterministic model offline: send four positive numbers, receive cleaned CP in watts, W′ in joules and kilojoules, the intermediate work totals, and the formula string.
What the two-point critical power model means
The two-parameter critical power model treats total mechanical work from a maximal constant-power effort as a straight line against duration: work equals critical power times time plus W′. Critical power (CP) is the slope—the asymptotic power the model says you could sustain indefinitely if fatigue were only about depleting the finite anaerobic reservoir. W′ is the intercept—the anaerobic work capacity in joules (often reported in kilojoules) that can be spent above CP before the effort fails.
For a physical fit the shorter effort should show a higher mean power than the longer one, which forces both CP and W′ to land positive. This calculator does not estimate power from heart rate, GPS, or speed, does not apply multi-parameter 3-minute all-out protocols, and does not prescribe training zones or race pacing charts. Always frame outputs as educational estimates from the two-point hyperbolic definition, not clinical diagnoses or race handicaps.
Where a two-point critical power calculator earns its keep
Secondary-school and college exercise-science courses often introduce critical power when teaching how mean power falls with duration, so a single trusted oracle that returns CP and W′ beside the formula string speeds grading and demo setup. Product teams building educational cycling or rowing widgets need a documented two-effort solve that clients can audit by hand rather than a black-box fitness score that mixes VO2 models without disclosure. Coaching platforms preparing synthetic athlete datasets need deterministic CP and W′ labels from known maximal efforts without network calls or model drift.
Race-preview tools sometimes display estimated time-to-exhaustion at a target power from CP and W′, but that derived use still starts from the same two-point parameters this capability returns cleanly. If you later need watts-per-kilogram ratios, speed-from-power estimates, VO2 max field tests, or multi-effort nonlinear CP fits, treat those as separate search intents and landings rather than overloading this two-point critical power page.
Always present results as educational estimates from the work equals CP times t plus W′ definition; training decisions require qualified coaches, local context, and protocols this tool does not collect.
What you can do with it
Classroom CP answer keys
Generate critical power and W′ from two maximal efforts so instructors and auto-graders share one transparent ground truth.
FAQ
How is critical power calculated from two efforts?
Example: 350 W for 300 s and 300 W for 1200 s → CP ≈ 283.33 W, W′ = 20000 J.
What units does the calculator use?
Durations must be in seconds (s) and mean powers in watts (W).
What happens if the two durations are equal?
The two-point model needs two distinct durations so the slope (CP) is defined.
Why must both CP and W′ come out positive?
For a physical hyperbolic fit the shorter maximal effort should have higher mean power than the longer one. Non-positive CP or W′ means the effort pair is inconsistent with the model and is rejected.
What does it cost?
The browser tool is free and runs locally.
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/health/critical-power-2point \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"duration_1":300,"power_1":350,"duration_2":1200,"power_2":300}'const res = await fetch("https://api.kit.forhosting.com/health/critical-power-2point", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"duration_1": 300,
"power_1": 350,
"duration_2": 1200,
"power_2": 300
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/health/critical-power-2point",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"duration_1": 300,
"power_1": 350,
"duration_2": 1200,
"power_2": 300
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/health/critical-power-2point", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"duration_1":300,"power_1":350,"duration_2":1200,"power_2":300}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"duration_1":300,"power_1":350,"duration_2":1200,"power_2":300}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/health/critical-power-2point", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"duration_1": 300,
"power_1": 350,
"duration_2": 1200,
"power_2": 300
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "health.critical_power_2point",
"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
Missing fields, non-numeric strings, equal durations, or effort pairs that yield non-positive CP or W′ fail with invalid_input instead of inventing fitness numbers.
What the two-point critical power model means
With two distinct maximal efforts you form two work totals work_1 equals power_1 times duration_1 and work_2 equals power_2 times duration_2, then solve CP equals (work_1 minus work_2) divided by (duration_1 minus duration_2) and W′ equals work_1 minus CP times duration_1. That algebra is identical to fitting a straight line through the two (duration, work) points; no iterative optimizer and no third effort are required.
Input contract, response shape, and error behaviour
A classic smoke check is three hundred seconds at three hundred fifty watts paired with twelve hundred seconds at three hundred watts, which yields critical power of approximately two hundred eighty-three point three three watts and W′ of twenty thousand joules (twenty kilojoules). Another check is one hundred eighty seconds at four hundred watts with seven hundred twenty seconds at three hundred twenty watts, which yields approximately two hundred ninety-three point three three watts and nineteen thousand two hundred joules. POST a JSON body with four required fields. The field duration_1 is the first maximal effort duration in seconds and must be a finite number strictly greater than zero; aliases t1, duration1, time_1, and seconds_1 are accepted. The field power_1 is the corresponding mean power in watts and must likewise be finite and strictly greater than zero; aliases p1, power1, watts_1, and mean_power_1 are accepted. The fields duration_2 and power_2 follow the same rules for the second effort, with aliases t2, duration2, time_2, seconds_2 and p2, power2, watts_2, mean_power_2. The two durations must differ; equal times make the denominator zero and fail with invalid_input. Missing fields, non-numeric strings, NaN, Infinity, zero, and negative values also fail with invalid_input and are not charged. On success the response returns the cleaned inputs, work_1 and work_2 in joules, critical_power in watts, w_prime in joules, w_prime_kj as W′ divided by one thousand, the formula string, method two_point_critical_power, unit_cp W, and unit_w_prime J. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where a two-point critical power calculator earns its keep
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
Coaching dashboard fixtures
Bulk-produce stable CP and W′ labels for athlete profiles and regression tests with hard invalid_input on bad efforts.
Educational power-meter widget demos
Show the two-point hyperbolic model from four numbers without mixing multi-parameter or VO2 models on the same landing.