Calculate active earth pressure from soil unit weight, wall height, and Ka, or solve for the missing value in the active earth pressure formula.
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Active Earth Pressure Formula
The calculator uses the active earth pressure resultant equation and rearranges it to solve for the missing value when you enter any 3 of the 4 fields.
- Pa = active earth pressure result entered or calculated by the tool
- gamma = unit weight of soil, converted to N/m³ for the calculation
- H = height of wall, converted to meters for the calculation
- Ka = coefficient of active earth pressure, unitless
If active earth pressure is missing, the calculator multiplies one-half by the soil unit weight, the square of the wall height, and Ka. If unit weight, wall height, or Ka is missing, it rearranges the same equation to isolate that variable. The calculator also converts the selected input units to base units before solving, then converts the result back to the unit selected in the missing field.
Typical Values and Unit Conversions for Active Earth Pressure
Common active earth pressure coefficients can be estimated from the Rankine relationship for level backfill and cohesionless soil. Actual design values depend on wall movement, backfill slope, drainage, surcharge, and soil testing.
| Soil friction angle, φ | Approx. Ka | General interpretation |
|---|---|---|
| 25° | 0.41 | Loose sand or lower-strength granular fill |
| 30° | 0.33 | Typical granular backfill estimate |
| 35° | 0.27 | Dense sand or well-compacted granular fill |
| 40° | 0.22 | Very dense granular material |
| Quantity | Supported units | Base conversion used |
|---|---|---|
| Active earth pressure | Pa, kPa, MPa, psi | 1 kPa = 1,000 Pa; 1 MPa = 1,000,000 Pa; 1 psi = 6,894.76 Pa |
| Unit weight of soil | N/m³, lb/ft³ | 1 lb/ft³ = 16.0185 N/m³ |
| Wall height | m, cm, ft, in | 1 cm = 0.01 m; 1 ft = 0.3048 m; 1 in = 0.0254 m |
Example Active Earth Pressure Calculations
Example 1: Calculate active earth pressure
Suppose the soil unit weight is 18,000 N/m³, the wall height is 4 m, and Ka is 0.33.
The calculator result is 47,520 Pa, or 47.52 kPa if kPa is selected.
Example 2: Calculate Ka
Suppose active earth pressure is 50,000 Pa, soil unit weight is 19,000 N/m³, and wall height is 4 m.
The coefficient of active earth pressure is approximately 0.329.
Active Earth Pressure Calculator FAQ
What is Ka in active earth pressure?
Ka is the coefficient of active earth pressure. It represents how much of the vertical soil pressure is converted into lateral pressure when a retaining wall moves enough for the soil to reach the active condition. For cohesionless soil with level backfill, Ka is often estimated from the soil friction angle, but project-specific design should use appropriate geotechnical data.
Why does wall height have such a large effect on the result?
The formula uses H², so active earth pressure increases with the square of the wall height. If the wall height doubles, the calculated value becomes four times larger, assuming the same soil unit weight and Ka.
What units should you enter?
You can enter the values in any supported units shown in the dropdowns. The calculator converts pressure to Pa, unit weight to N/m³, and height to meters before solving. Ka has no units, so you should enter it as a decimal such as 0.33, not 33 percent.