# Earth Pressure Calculator

All three coefficients at once; the gap between active and passive is where the money is.

- Page: https://jianzhujisuan.com/en/earth-pressure
- Category: Foundations (https://jianzhujisuan.com/en/c/foundations)
- Chinese version: https://jianzhujisuan.com/zh/earth-pressure.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Friction angle φ 30 °, Unit weight γ 18 kN/m³, Wall height or depth 4 m, Case Active (wall moves away)): **Total thrust per metre 48.0 kN/m**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Friction angle φ | number | 30 | ° |  |
| Unit weight γ | number | 18 | kN/m³ |  |
| Wall height or depth | number | 4 | m |  |
| Case | select | Active (wall moves away) | — |  |

## Formula

- **At rest**: K0 = 1 − sinφ (Jaky)
- **Active**: Ka = tan²(45 − φ/2)
- **Passive**: Kp = tan²(45 + φ/2)
- **Pressure at base**: p = K·γ·H
- **Total thrust**: P = 0.5·K·γ·H²
- **Resultant height**: y = H/3 above base

## Worked example

φ 30°, γ 18 kN/m³, 4 m wall, active case: K0 0.500, Ka 0.333, Kp 3.000, Kp/Ka 9.0, 24 kPa at the base, 48 kN/m total thrust acting 1.33 m above the base.

### Friction angle quick reference (γ = 18 kN/m³, 4 m wall, active case, all three coefficients side by side)

| Friction angle φ (°) | At rest K0 | Active Ka | Passive Kp | Kp / Ka | Pressure at base (kPa) | Thrust per metre (kN/m) |
|---|---|---|---|---|---|---|
| 20 | 0.658 | 0.490 | 2.040 | 4.2 | 35.3 | 70.6 |
| 25 | 0.577 | 0.406 | 2.464 | 6.1 | 29.2 | 58.4 |
| 30 | 0.500 | 0.333 | 3.000 | 9.0 | 24.0 | 48.0 |
| 35 | 0.426 | 0.271 | 3.690 | 13.6 | 19.5 | 39.0 |
| 40 | 0.357 | 0.217 | 4.599 | 21.1 | 15.7 | 31.3 |
| 45 | 0.293 | 0.172 | 5.828 | 34.0 | 12.4 | 24.7 |

From φ 20 to 45 degrees, Ka only falls from 0.490 to 0.172, a factor of 2.8, while Kp rises from 2.040 to 5.828, also about 2.9 — because Kp = 1/Ka, so the ratio moves as the square. Quoting the friction angle 5 degrees high therefore cuts the active thrust linearly (25 to 30 degrees takes it from 58.4 to 48.0, an 18% saving) but changes the passive resistance quadratically. Ask the investigation whether the φ given is peak or residual, and drained or undrained: two values for the same layer can differ by 10 degrees.

### What groundwater does: dry, total stress and effective stress on the same wall (H = 6 m, water table 2 m down, φ 30 degrees)

| Case | Soil pressure at base (kPa) | Water pressure (kPa) | Total (kPa) | vs dry |
|---|---|---|---|---|
| Dry (unit weight 18 throughout, no water) | 36.0 | 0.0 | 36.0 | — |
| Below water table, total stress (Ka × saturated unit weight 20) | 40.0 | included above | 40.0 | +11% |
| Below water table, effective stress (submerged 10.19 + hydrostatic) | 25.6 | 39.2 | 64.8 | +80% |

**Multiplying the saturated unit weight by Ka below the water table is the commonest excavation error there is.** The soil skeleton carries effective stress and the water carries only hydrostatic pressure, so the two are computed separately. In the example above, effective stress gives 64.8 kPa total against 40.0 kPa for the total-stress shortcut — **38% short**, and the shortcut is simply invalid in sand. Cohesive soil may be treated in total stress, but then the total-stress strength parameters (cu, φu) must be used, never effective strength paired with a saturated unit weight. Where there is an aquifer, silty sand, or artesian water under the base, base heave and piping need their own check — this table does not cover them.


## Questions

### How much bigger is passive than active pressure?

Numerically Kp is 1/Ka, so the ratio is 1/Ka² — about 4.2 times at phi 20 degrees, 9 times at 30 and 21 times at 40. The friction angle drives it. That gap has real consequences in an excavation: the retained side is active and the resisting side in front of the toe is passive, so a small movement into the soil mobilises a lot of resistance — provided the movement is acceptable.
### How is earth pressure calculated when there is groundwater?

Effective stress: above the water table take the bulk unit weight times Ka; below it take the submerged unit weight (saturated minus 9.81) times Ka; then add the hydrostatic triangle γw·h separately and sum the two. In the H = 6 m, 2 m water table example on this page that gives 64.8 kPa, against 40.0 kPa for multiplying the saturated unit weight by Ka directly. Sand must be done in effective stress; cohesive soil may be done in total stress but then it needs total-stress strength parameters. Never mix the two.

### Why can't passive pressure be used directly for anchor capacity?

Because it needs movement. Full passive resistance requires the wall to push 2-5% of its height into the soil — 12 to 30 cm on a 6 m excavation. The wall has moved nothing like that when the anchors are stressed, so a capacity computed from Kp is overstated and the anchor will not hold. Practice applies a reduction of 0.5-0.7 to Kp, or designs on at-rest pressure with a factor of safety. It is in JGJ 120 and most excavation manuals, and it is still the thing most often missed on site.


## Related tools

- [Pile Capacity Calculator](https://jianzhujisuan.com/en/pile-capacity): N value for sand, cu for clay: shaft and base worked separately, then divided by a factor of safety.
- [Bearing Capacity Calculator](https://jianzhujisuan.com/en/bearing-capacity): The three bearing factors follow from the friction angle; divide the ultimate value by a factor of safety.
- [Retaining Wall Stability Calculator](https://jianzhujisuan.com/en/retaining-wall): Soil and surcharge produce moments at different heights; both factors of safety must pass.

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