Immersed weight calculator
A 50 N object displacing 0.002 m³ of water at 1000 kg/m³ reads 30.38 N on a scale, because the water pushes up with 19.62 N. Enter true weight, volume and fluid density; gravity defaults to 9.81 m/s². Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- True weight
- 50
- Volume
- 0.002
- Fluid density
- 1,000
- Gravity
- 9.81
- Buoyant force
- 19.62 N
- Immersed weight
- 30.38
- Apparent weight
- 30.38
- Equation
- W_immersed = 50 − 1000 · 0.002 · 9.81 = 30.38
An immersed weight calculator converts true weight, displaced volume, and fluid density into the apparent weight of an object sitting in a liquid or gas. Archimedes' principle says the surrounding fluid pushes up with a buoyant force equal to the weight of the fluid displaced, so a scale reading drops by that amount: immersed weight equals true weight minus density times volume times gravity. Enter true weight in newtons, volume in cubic metres, and fluid density in kilograms per cubic metre; optional gravity defaults to 9.81 metres per second squared so SI inputs yield newtons.
What immersed (apparent) weight means under Archimedes' principle
Apparent weight, often called immersed weight in hydrostatics, is the net downward force a scale would read if the object were weighed while surrounded by a fluid instead of in vacuum or dry air. Archimedes' principle states that a body immersed in a fluid feels an upward buoyant force equal to the weight of the fluid it displaces. In a uniform gravitational field that buoyant force is the product of fluid density, displaced volume, and gravitational acceleration: F_b equals rho times V times g.
True weight is the gravitational force on the object, already in newtons when mass in kilograms is multiplied by g; volume is the exterior volume of the submerged portion in cubic metres for SI work; fluid density is the mass per unit volume of the surrounding liquid or gas, about one thousand kilograms per cubic metre for liquid water near room temperature and far smaller for air.
Gravity sets the scale of the buoyant term: Earth-standard problems often use nine point eight one metres per second squared, which is the default when the gravity field is omitted. When buoyancy exceeds true weight the immersed weight is negative, which is the mathematical signal that the object would float or accelerate upward if unconstrained. Negative fluid density is not a physical continuum property in this model and is rejected rather than silently producing a downward buoyancy.
Zero density or zero volume yields immersed weight equal to true weight, matching a weighing in vacuum or with nothing displaced.
FAQ
How is immersed weight calculated?
Immersed (apparent) weight is W_immersed = W_true − ρ V g. True weight is the dry gravitational force, ρ is fluid density, V is displaced volume, and g is gravitational acceleration (default 9.81 m/s²). The result is in newtons when SI units are used.
What happens if fluid density is negative?
Fluid density must not be negative; a negative ρ is treated as a domain error, not a signed buoyancy, and failed validation is not billed.
Why is gravity needed if true weight is already in newtons?
True weight is a force, but the buoyant term ρ V is a mass until it is multiplied by g. Optional gravity defaults to 9.81 so SI density and volume produce a force in newtons that can be subtracted from W_true.
What does the immersed weight calculator cost?
The browser tool is free and runs locally.
Can the immersed weight be negative?
Yes. A negative result means the buoyant force is larger than the true weight, so the object would float or rise if nothing held it down. A value of zero means it is exactly balanced.
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/phys/immersed-weight \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"true_weight":50,"volume":0.002,"fluid_density":1000}'const res = await fetch("https://api.kit.forhosting.com/phys/immersed-weight", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"true_weight": 50,
"volume": 0.002,
"fluid_density": 1000
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/immersed-weight",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"true_weight": 50,
"volume": 0.002,
"fluid_density": 1000
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/immersed-weight", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"true_weight":50,"volume":0.002,"fluid_density":1000}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"true_weight":50,"volume":0.002,"fluid_density":1000}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/immersed-weight", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"true_weight": 50,
"volume": 0.002,
"fluid_density": 1000
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.immersed_weight",
"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
Negative fluid density is rejected as invalid_input.
What immersed (apparent) weight means under Archimedes' principle
Subtract that upward force from the object's true weight and you obtain the immersed weight: W_immersed equals W_true minus rho V g.
How to call the API and what comes back
Volume must not be negative for the same reason; zero volume is allowed and simply returns the true weight. Formula and equation strings restate the subtraction for worksheets, and steps list the given values, the Archimedes product, and the final difference. Send a JSON body with three required finite numbers: true_weight (aliases weight, W), volume (aliases V, displaced_volume, vol), and fluid_density (aliases density, rho). Gravity is optional (aliases g, g_accel, gravitational_acceleration) and defaults to 9.81 metres per second squared so that SI inputs in newtons, cubic metres, and kilograms per cubic metre return newtons without an extra required field. Absolute values 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. Fluid density must not be negative: a strictly negative rho triggers invalid_input and is never billed, because a negative density is almost always a sign error or a swapped column rather than a physical fluid. On success the response echoes the rounded inputs including the gravity actually used, reports buoyant_force as rho times V times g, and sets immersed_weight and apparent_weight to the same rounded difference W_true minus that buoyant force. Failed validation—missing fields, non-finite numbers, values outside absolute limits, negative density, negative volume, or a non-finite product—returns invalid_input. Pricing is a flat $0.002 per successful request with unit item.
Practical tips, units, limits, and related searches
Keep true weight, volume, density, and gravity inside the published absolute range so the product and the difference cannot overflow into a non-finite immersed weight the solver must reject. Use consistent units: kilograms per cubic metre, cubic metres, and metres per second squared with true weight already in newtons yield newtons. Grams, centimetres, or pound-force require a coherent gravity and a true weight in the same force unit; this tool does not convert units, estimate partial submersion from freeboard, or look up fluid properties from a name such as seawater. Prefer this capability when you already have true weight, displaced volume, and fluid density and only need the apparent weight in newtons. Prefer sending JSON numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern. When teaching, pair examples: fifty newtons, two thousandths of a cubic metre of water at one thousand kilograms per cubic metre, and g equals nine point eight one yields a buoyant force of about nineteen point six two newtons and an immersed weight of about thirty point three eight newtons; a deliberate negative density demonstrates the hard invalid_input path. This landing targets people searching for an immersed weight calculator, apparent weight in a fluid, or submerged weighing net force tool online; it is not a ship hydrostatics package, not a CFD solver, and not a unit converter. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately send a negative density. Round-trip checks are easy: recompute density times volume times gravity, subtract from true weight, and confirm it equals immersed_weight within the same twelve-decimal rounding. API automation costs $0.002 per successful item.
Integration use cases
Homework checks for apparent-weight problems
Students enter textbook true weight, displaced volume, and fluid density, then compare hand-written immersed weight and substitution steps against a deterministic API or browser result before submitting.
Submerged-weighing lab reductions
Lab notebooks subtract ρ V g from a dry weight to obtain the scale reading in water or oil, pin expected newtons, and flag a negative density as invalid_input instead of a silent sign flip.
Net downward force on submerged equipment
Engineering scripts estimate the remaining downward force on a fixture, sinker, or tank insert from known true weight, exterior volume, and fluid density before choosing supports or ballast.
Technical questions
Can immersed weight be negative?
Yes. If ρ V g exceeds true weight, immersed_weight is negative. That signed result means buoyancy would lift the object if it were unconstrained; the calculator does not clamp the value to zero.