Engineering lesson
Convert mud weight to pressure gradient with units shown
In US field units, multiply mud weight in ppg by 0.052 to obtain a hydrostatic gradient in psi/ft. Multiply that gradient by the vertical fluid height to obtain a pressure difference.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Follow the units through the conversion
A pound per US gallon is a density expressed as weight per volume. The field coefficient incorporates the gallon-to-cubic-inch conversion and twelve inches per foot. Its rounded value is convenient for drilling worksheets; it is not a dimensionless universal constant.
For water at 8.33 ppg, the worksheet gives 0.43316 psi/ft. A 10 ppg fluid gives 0.520 psi/ft. The higher density increases pressure at every fixed vertical depth, but a gradient alone does not specify a bottomhole pressure.
A gradient is a rate of pressure change
Pressure divided by depth has units of psi/ft. Pressure itself has units of psi. A result of 0.52 must therefore carry its gradient unit; calling it 0.52 psi drops the length denominator and changes the quantity.
Use TVD or a vertical interval for hydrostatic head. A horizontal pipe can contain substantial fluid volume while contributing almost no vertical hydrostatic head. Measured length belongs in the capacity calculation.
Convert the quantity before choosing a coefficient
For SI inputs use density in kg/m³, gravitational acceleration in m/s² and vertical height in m. Their product is pascals. Do not multiply kg/m³ by the field coefficient 0.052.
A uniform density is assumed here. Temperature-dependent density, mixed fluids and compressible columns require a section sum or integration rather than one surface density multiplied by the entire depth.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Mud weight (ppg) = 10. Gradient (psi/ft): 0.52; Fluid head (psi): 4160.
- Gradient (psi/ft)
Worked example
Mud weight, gradient and fluid head
Uniform mud, 8,000 ft vertical height, no added surface pressure. Mud weight is the only changing input.
Relation and unit basis
gradient = 0.052 MW; ΔP = gradient × TVD
MW in ppg, gradient in psi/ft, TVD in ft, ΔP in psi. The rounded field coefficient assumes these units.
1. Define the baseline
Mud weight (ppg) = 10
Uniform mud, 8,000 ft vertical height, no added surface pressure. Mud weight is the only changing input.
2. Select the relation
gradient = 0.052 MW; ΔP = gradient × TVD
MW in ppg, gradient in psi/ft, TVD in ft, ΔP in psi. The rounded field coefficient assumes these units.
3. Substitute the values
0.052 × 10 = 0.520 psi/ft; 0.520 × 8,000 = 4,160 psi
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Gradient (psi/ft) = 0.52; Fluid head (psi) = 4160
Fluid head is a pressure difference. A top boundary pressure would be added separately.
Result and interpretation
Gradient (psi/ft) = 0.52; Fluid head (psi) = 4160
Fluid head is a pressure difference. A top boundary pressure would be added separately.
Compare the gradient first, then the pressure at a fixed 8,000 ft TVD. The two output columns distinguish these quantities.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Mud weight (ppg) | Gradient (psi/ft) | Fluid head (psi) |
|---|---|---|
| 8 | 0.416 | 3,328 |
| 9 | 0.468 | 3,744 |
| 10 | 0.52 | 4,160 |
| 11 | 0.572 | 4,576 |
| 12 | 0.624 | 4,992 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. What gradient and pressure result from 11 ppg over 6,000 ft TVD?
Show the worked answer
Gradient = 0.052 × 11 = 0.572 psi/ft. Pressure increase = 0.572 × 6,000 = 3,432 psi.
2. Reproduce the baseline Gradient (psi/ft) without rounding intermediate values.
Show the worked answer
0.052 × 10 = 0.520 psi/ft; 0.520 × 8,000 = 4,160 psi. Gradient (psi/ft) = 0.52. Fluid head is a pressure difference. A top boundary pressure would be added separately.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Mud weight (ppg) changes from 8 to 12. Other controls remain as stated in the premise. Gradient (psi/ft) changes from 0.416 to 0.624.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. MW in ppg, gradient in psi/ft, TVD in ft, ΔP in psi. The rounded field coefficient assumes these units. Fluid head is a pressure difference. A top boundary pressure would be added separately.
Before using the result
- Record ppg as lb per US gallon.
- Keep psi/ft on the gradient.
- Use vertical fluid height for head.
Fluid head is a pressure difference. A top boundary pressure would be added separately.
Continue learning
Start with the broader workflow guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.