Earth Pressure Calculator
All three coefficients at once; the gap between active and passive is where the money is.
Also known as lateral earth pressure · rankine earth pressure · Ka Kp K0
With the default inputs: Friction angle φ 30° · Unit weight γ 18 kN/m³ · Wall height or depth 4 m etc.Total thrust per metre 48.0 kN/m
Use your own dimensions ↓Inputs
Result
| At rest K0 | 0.500 |
| Active Ka | 0.333 |
| Passive Kp | 3.000 |
| Kp over Ka | 9.0× |
| Coefficient used | 0.333 |
| Pressure at base | 24.0kPa |
| Resultant height (from wall base) | 1.33m |
How this is worked out
The three coefficients describe three displacement states and picking the wrong one changes the answer several fold. At rest, K0, applies when the wall does not move at all, such as a basement wall between rigid floors; Jaky gives K0 = 1 - sin phi and it is the conservative no-movement case. Active, Ka, is the wall moving away until the soil shears, tan²(45 - phi/2), the normal design value for retaining walls. Passive, Kp, is the wall pushing into the soil, tan²(45 + phi/2), numerically 1/Ka. At phi 30 degrees Ka is 0.333 and Kp is 3.0, a factor of nine. That is exactly why passive pressure cannot be used freely: it needs wall movement of 2-5% of the height to mobilise, and in an excavation the wall has already deflected before the props go in. Design on something between K0 and Ka, and when you do use Kp, apply a reduction of 0.5 to 0.7 because Rankine over-predicts it.
Next up: Pile Capacity Calculator · Bearing Capacity Calculator
Reverse: known result, work out one input
Enter a target result; the other inputs stay fixed and this one is worked out.
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 |
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.
Basis
- Rankine earth pressure theory — Ka = (1 − sinφ)/(1 + sinφ) for a vertical wall with level backfill
- GB 50007-2011, Table 6.7.5-1 — wall friction angle δ as a fraction of φk
- GB 50007-2011, §6.7.5 — the sliding and overturning checks that use these coefficients
FAQ
How much bigger is passive than active pressure?
How is earth pressure calculated when there is groundwater?
Why can't passive pressure be used directly for anchor capacity?
What to calculate next
These jobs are done back to back on site — follow the steps to work through the whole sequence.
Retaining: pressure to supportStep 1 of 4
- 1Earth Pressure Calculator
- 2Retaining Wall Stability Calculator
- 3Soldier Pile Calculator
- 4Ground Anchor Calculator
Cite this page
Use this format in reports, method statements or coursework. The link is permanent.
Building Calculator. Earth Pressure Calculator. 2026-10-25. https://jianzhujisuan.com/en/earth-pressure