Earthquake energy ratio between magnitudes calculator
A magnitude 7 earthquake releases about 998.56 times the energy of a magnitude 5, because each whole step multiplies energy by roughly 31.6. Enter two magnitudes in any order to see the gap behind numbers that look close. Free in your browser.
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Worked example
- Magnitude 1
- 7
- Magnitude 2
- 5
- Higher magnitude
- 7
- Lower magnitude
- 5
- Magnitude difference
- 2
- Energy ratio
- 998.56
This earthquake energy ratio calculator compares two magnitudes and estimates how many times more energy the stronger earthquake released. It uses the standard approximation that each whole magnitude step corresponds to a 31.6-fold increase in released energy. Enter both magnitudes in the same magnitude scale, and the result identifies the higher value, finds the absolute difference, and applies the exponential relationship. The calculation is useful for quickly interpreting magnitude numbers that otherwise look deceptively close together.
Why a small magnitude difference means a large energy difference
Earthquake magnitude scales are logarithmic, so magnitude values cannot be compared as though they were ordinary linear measurements. A magnitude 7 earthquake is not merely a little stronger than a magnitude 6 earthquake. Using the energy approximation in this calculator, a one-unit increase represents about 31.6 times as much released energy.
A two-unit increase compounds that factor, producing roughly 998.56 times as much energy. This rapid growth explains why apparently modest gaps between earthquake reports can describe events with dramatically different physical consequences. The calculator makes that relationship explicit by first placing the two entered magnitudes in higher-to-lower order.
It then subtracts the lower magnitude from the higher magnitude and raises 31.6 to that difference. The returned energy ratio always describes the larger-energy event relative to the smaller-energy event, so it is at least one. If both values are equal, their magnitude difference is zero and the estimated ratio is exactly one.
This comparison concerns released energy only; it does not predict damage, shaking at a particular location, casualties, or tsunami risk.
How to enter and interpret the two magnitudes
Enter one finite numerical magnitude in each field. The order does not matter because the calculator identifies the higher and lower values before computing the ratio. For example, entering 5 and 7 gives the same larger-to-smaller energy comparison as entering 7 and 5.
Decimal magnitudes are supported, which is important because a half-unit difference is already substantial on a logarithmic scale. Use values reported on the same magnitude scale and under comparable measurement conventions. Modern reports commonly use moment magnitude, but historical catalogs and specialized reports may use other magnitude measures.
Combining unlike scales can create a mathematically valid number that is not a sound scientific comparison. The result includes both original inputs, the ordered magnitudes, their absolute difference, the energy ratio, and the fixed factor of 31.6 used per magnitude unit. Read an energy ratio of 31.6 as an estimate that the higher-magnitude earthquake released 31.6 times the energy of the lower-magnitude earthquake.
The ratio is an approximation, not a direct measurement in joules, because it derives only from the reported magnitude difference.
What the result can and cannot tell you
The result is best used for scale, education, catalog comparisons, and quick checks in reporting or analysis. It translates an abstract magnitude gap into an intuitive multiplier without requiring the absolute energy of either earthquake. That makes it useful when comparing two catalog entries, reviewing a sequence of events, explaining why magnitude differences matter, or checking a value used in an article or classroom exercise.
However, energy release is only one part of earthquake impact. The shaking experienced by people and structures also depends on depth, distance from the rupture, local geology, rupture direction, building design, and many other conditions. A lower-magnitude event close to a vulnerable community may cause more local damage than a larger event far away or deep underground.
The calculator therefore should not be used as a hazard forecast or emergency decision tool. It also does not convert magnitude into an exact energy value; it reports a relative estimate based on the fixed 31.6-per-unit factor requested by this method.
What you can do with it
Compare two earthquake reports
Turn the difference between two reported magnitudes into a clear larger-to-smaller energy multiplier.
Explain logarithmic magnitude scales
Show students or readers why a one-unit or two-unit magnitude gap represents a dramatic change in released energy.
Check catalog analysis
Verify a relative-energy figure before using it in a dataset, report, presentation, or editorial workflow.
FAQ
Does the order of the magnitudes matter?
No. The calculator orders the values and reports the energy of the higher-magnitude earthquake relative to the lower-magnitude earthquake.
What happens when both magnitudes are equal?
The magnitude difference is zero, so the estimated energy ratio is one.
Can I compare decimal magnitudes?
Yes. Both inputs may be finite decimal numbers, and the exponential formula applies to their full difference.
Does the ratio predict earthquake damage?
No. It compares estimated released energy only. Damage and felt shaking also depend on location, depth, geology, construction, and other conditions.
How much more energy does one magnitude step mean?
About 31.6 times as much released energy for each whole unit. Two units compound to roughly 998.56 times, which is why a gap that looks small on paper can describe very different earthquakes.
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/earth/magnitude-energy-ratio \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"magnitude_1":7,"magnitude_2":5}'const res = await fetch("https://api.kit.forhosting.com/earth/magnitude-energy-ratio", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"magnitude_1": 7,
"magnitude_2": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/earth/magnitude-energy-ratio",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"magnitude_1": 7,
"magnitude_2": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/earth/magnitude-energy-ratio", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"magnitude_1":7,"magnitude_2":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"magnitude_1":7,"magnitude_2":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/earth/magnitude-energy-ratio", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"magnitude_1": 7,
"magnitude_2": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "earth.magnitude_energy_ratio",
"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
What the result can and cannot tell you
For automated comparisons, the API performs the same deterministic calculation for $0.002 per request and rejects input when either magnitude is missing or is not a finite number.
Technical questions
What formula does the calculator use?
It calculates 31.6 raised to the absolute difference between the two magnitudes: energy ratio = 31.6^|magnitude_1 - magnitude_2|.
How much does the API calculation cost?
Each API request costs $0.002. The same deterministic calculation is available free in the browser.