# Earthquake Calculator Guide: Magnitude, Energy, Distance, and Shaking

Use earthquake math carefully: compare magnitude energy, estimate distance from P-S delay, and model simplified shaking intensity with clear limits.

---

- **Canonical URL:** https://dothecalculation.com/blog/hobby/earthquake-calculator-guide
- **Category:** Hobbies & Leisure Utilities
- **Author:** Do The Calculation Team
- **Published:** 2026-06-08
- **Last updated:** 2026-07-03
- **Reading time:** 18 min read
- **Publisher:** Do The Calculation (https://dothecalculation.com)
- **Methodology:** https://dothecalculation.com/methodology

---

## The Calculator Has Three Separate Earthquake Modes

The Do The Calculation earthquake tool is not one single earthquake answer. It has three educational modes: magnitude-to-energy comparison, epicenter distance from P-S wave delay, and a simplified ground-shaking estimate. Keep those modes separate. Energy describes the source event, distance uses wave arrival timing, and intensity describes local shaking at a site.

_[Figure: Pick the right earthquake calculation — Each mode answers a different scientific question.]_

## Magnitude and Energy: Why One Whole Number Matters

The energy mode uses the common logarithmic relationship E = 10^(1.5M + 4.8), with E in joules. That means each one-unit magnitude increase multiplies estimated energy by about 31.6 and wave amplitude by 10 when two magnitudes are compared. This is why a magnitude 6 is not just slightly larger than a magnitude 5.

**Energy formula used by the calculator**

```
Energy in joules = 10^(1.5 x magnitude + 4.8)
```
- TNT tons = joules / 4.184e9.
- Energy ratio = 10^(1.5 x magnitude difference).
- Amplitude ratio = 10^(magnitude difference).

**Magnitude 6 compared with magnitude 5**
| Metric | Calculator output |
| --- | --- |
| Magnitude being evaluated | 6.0 |
| Comparison magnitude | 5.0 |
| Energy | 63,095,734,448,019 J |
| TNT equivalent | 15,080.24 tons |
| Energy ratio | 31.62x |
| Amplitude ratio | 10x |

_[Figure: A one-magnitude increase is not linear — The calculator returns the same ratios for 6 vs 5 and 7 vs 6.]_

## Distance from P-S Delay

P waves usually arrive before S waves. The calculator estimates distance from the time gap between those arrivals using the selected P-wave and S-wave velocities. With the default 6.0 km/s P-wave velocity and 3.5 km/s S-wave velocity, a 10-second S-minus-P delay returns an 84 km distance estimate.

**P-S distance estimate**

```
Distance = delay x (Vp x Vs) / (Vp - Vs)
```
- Vp is P-wave velocity.
- Vs is S-wave velocity.
- If Vp is not greater than Vs, the calculator returns zero distance.

**Distance example verified against calculateEarthquakeDistance**
| Input or result | Value |
| --- | --- |
| P-S delay | 10 seconds |
| P-wave velocity | 6.0 km/s |
| S-wave velocity | 3.5 km/s |
| Estimated distance | 84.0 km |
| P travel time | 14.0 seconds |
| S travel time | 24.0 seconds |

## Shaking Intensity Is Site-Specific

The intensity mode estimates simplified peak ground acceleration from magnitude, distance, focal depth, and soil type. It then maps PGA thresholds to a Modified Mercalli-style class. This is a teaching model. Real ground motion depends on fault geometry, rupture direction, basin effects, building type, local geology, and recorded waveform data.

**Simplified PGA model**

```
hypocentral distance = sqrt(distance^2 + depth^2)

ln(PGA) = -2.5 + 1.2M
  - 1.5 ln(hypocentral distance) + soil factor
```
- Soil factor is 0 for rock, 0.2 for stiff soil, and 0.5 for soft soil.
- PGA is reported as percent of gravity.

**Intensity example: M6.5, 30 km, stiff soil, 10 km depth**
| Metric | Calculator output |
| --- | --- |
| PGA | 1.38%g |
| MMI class | IV |
| Shaking label | Light |
| Damage label | None |

_[Figure: Magnitude, distance, and intensity are different — Do not mix the meaning of these outputs.]_

## Safety Limits and Prediction Limits

This calculator is for education, scenario comparison, and understanding earthquake math. It cannot predict earthquakes. USGS states that scientists cannot predict the exact date, time, location, and magnitude of a future major earthquake. For preparedness, alerts, and hazard decisions, use official geological and emergency-management sources.

> **Do not use this as an emergency tool** — If you feel shaking or receive an official alert, follow local emergency guidance. Calculator outputs are not a substitute for alerts, hazard maps, building codes, or professional seismology.

Tool: [Open the Earthquake Magnitude & Energy Calculator](https://dothecalculation.com/calculators/earthquake-calculator) — Compare earthquake energy, estimate P-S delay distance, and explore simplified shaking intensity scenarios.

## Official Sources Checked

- USGS earthquake prediction FAQ: https://www.usgs.gov/faqs/can-you-predict-earthquakes
- USGS earthquake travel times: https://www.usgs.gov/programs/earthquake-hazards/earthquake-travel-times
- USGS P-wave and S-wave paths: https://www.usgs.gov/media/images/p-wave-and-s-wave-paths-through-earth

## Earthquake Calculator FAQ

**Can this calculator predict earthquakes?**

No. It models educational scenarios after you enter assumptions; it cannot predict future earthquakes.

**Why does one magnitude step matter so much?**

The calculator uses a logarithmic relationship, so one magnitude unit means about 10x amplitude and 31.6x energy.

**What is the energy formula?**

Energy in joules equals 10 raised to the power of 1.5 times magnitude plus 4.8.

**What does P-S delay mean?**

It is the time difference between the first P-wave arrival and the S-wave arrival at a station.

**Why must P-wave velocity be greater than S-wave velocity?**

The distance formula depends on P waves arriving first; if the velocity order is invalid, the calculator returns zero distance.

**What is PGA?**

PGA means peak ground acceleration, reported here as a percentage of gravity.

**What does MMI mean?**

MMI refers to Modified Mercalli-style intensity classes describing local shaking effects.

**Does soil type affect shaking?**

Yes. The simplified model adds a soil factor for stiff and soft soil, which increases estimated PGA.

**Why can the same earthquake feel different in different places?**

Distance, depth, soil, structures, basin effects, and rupture direction can all change local shaking.

**Should I use this for safety decisions?**

No. Use official alerts, hazard maps, emergency guidance, and professional engineering or seismology resources.

---

_Source: [Do The Calculation](https://dothecalculation.com/blog/hobby/earthquake-calculator-guide). Quote freely with attribution and a link to this page._