Calculate missing wellhead pressure, bottom hole pressure, well depth, gas specific gravity, or average temperature from four inputs.

Wellhead Pressure Calculator

Enter any 4 values to calculate the missing variable






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Understanding Wellhead Pressure

The wellhead pressure is the pressure observed at the surface of the well. In a static gas column, it will normally be lower than the bottom-hole pressure because some of the pressure is used to support the gas column between the reservoir and the wellhead. This calculator is designed for quick engineering estimates using bottom-hole pressure, true vertical depth, gas specific gravity, and average temperature.

It is most useful for static or near-static gas conditions, fast field checks, and validating whether an entered pressure profile is directionally reasonable.

Wellhead Pressure Formula

The calculation is based on the exponential gas-column relationship below:

P₍wh) = (P₍bh)) / (e⁽(0.01875 S_g H) / (Z Tₐᵥ)))

In this equation, Pwh is the wellhead pressure, Pbh is the bottom-hole pressure, H is true vertical depth, Sg is gas specific gravity, Tav is the average absolute temperature, and Z is the gas compressibility factor. This calculator assumes Z = 1, so the result should be treated as an approximation for a static gas column rather than a full real-gas wellbore model.

The constant 0.01875 is the field-unit factor used when depth is in feet, temperature is in Rankine, and pressure is in psia.

Input Definitions

Input Meaning Practical Note
Bottom Hole Pressure Absolute pressure at the bottom of the wellbore. Use absolute pressure for hand checks. Gauge pressure must be converted first.
True Vertical Well Depth Vertical distance from surface reference to the bottom-hole location. Use TVD, not measured depth, especially in deviated or horizontal wells.
Specific Gravity of Gas Gas density relative to air at standard conditions. Higher gas specific gravity means a heavier gas column and a lower surface pressure.
Average Temperature Average gas temperature over the vertical column. The equation uses absolute temperature internally. The calculator handles unit conversion for you.
Wellhead Pressure Surface pressure at the top of the well. This is the unknown most users are solving for, but the calculator can also back-calculate another variable.

How Each Variable Changes the Result

Change Effect on Wellhead Pressure Why
Higher bottom-hole pressure Increases wellhead pressure A larger starting pressure at depth raises the entire pressure profile.
Greater true vertical depth Decreases wellhead pressure A taller gas column creates a larger pressure drop from bottom to surface.
Higher gas specific gravity Decreases wellhead pressure Heavier gas produces a larger static gradient.
Higher average temperature Increases wellhead pressure Hotter gas is less dense, so the column weighs less.

Useful Rearrangements

If you know four values and want to solve manually for the fifth, the same relationship can be rearranged as follows:

P₍bh) = P₍wh) e⁽(0.01875 S_g H) / (Z Tₐᵥ))
H = (Z Tₐᵥ) / (0.01875 S_g)ln((P₍bh)) / (P₍wh)))
S_g = (Z Tₐᵥ) / (0.01875 H)ln((P₍bh)) / (P₍wh)))
Tₐᵥ = (0.01875 S_g H) / (Z ln((P₍bh)) / (P₍wh))))

How to Use the Calculator

  1. Enter the bottom-hole pressure.
  2. Enter the true vertical well depth.
  3. Enter the gas specific gravity.
  4. Enter the average temperature for the gas column.
  5. Leave the unknown field blank and calculate.
  6. Check that the result makes physical sense before using it in design or operations decisions.

Example

For a bottom-hole pressure of 1500 psia, true vertical depth of 8000 ft, gas specific gravity of 0.65, and average temperature of 520 °R, the estimated wellhead pressure is:

P₍wh) = (1500) / (e⁽(0.01875 × 0.65 × 8000) / (520))) ≈ 1244

So the wellhead pressure is approximately 1244 psia. Under these assumptions, the gas column accounts for about 256 psi of pressure difference between the bottom hole and the surface.

Important Assumptions

  • The well contains a static gas column.
  • The average temperature is reasonably representative of the full column.
  • The gas compressibility factor is taken as 1.
  • The depth used is true vertical depth, not measured depth.
  • Pressures are interpreted on an absolute basis in the underlying equation.

Common Input Mistakes

  • Using psig instead of psia. If you are hand-checking a field reading, convert gauge pressure to absolute pressure first.
  • Using measured depth instead of TVD. This can overstate the gas-column effect in deviated wells.
  • Entering bottom-hole temperature instead of average column temperature. The equation uses the average temperature over the gas column.
  • Applying the equation to flowing or multiphase wells. Friction, liquid loading, and changing fluid composition can make the estimate unreliable.
  • Ignoring non-ideal gas behavior. At higher pressures, assuming Z = 1 may introduce noticeable error.

Pressure Conversion Reminder

If your pressure reading is in gauge pressure and you want to verify the calculation by hand, convert to absolute pressure first:

P₍abs) = P₍gauge) + 14.7

This is the standard sea-level approximation. The calculator itself handles unit conversions, but understanding the distinction helps prevent unrealistic results.

When This Calculator Is Most Useful

  • Estimating surface pressure from a known bottom-hole pressure in a gas well
  • Checking whether a reported wellhead pressure is directionally reasonable
  • Comparing the effect of depth, gas gravity, or temperature on surface pressure
  • Performing quick hand-checks before using more detailed wellbore or nodal analysis software

When a More Advanced Model Is Better

  • Flowing wells with meaningful friction losses
  • Multiphase wells containing gas, oil, water, or condensate
  • High-pressure systems where real-gas compressibility is important
  • Wells with strong temperature variation along the wellbore
  • Situations requiring operational accuracy rather than a first-pass estimate

Quick Interpretation Guide

If your calculated wellhead pressure comes out higher than the bottom-hole pressure for a normal positive depth, that is usually a sign that one of the inputs is inconsistent, the pressure basis is wrong, or the static-gas assumption does not apply. In most static gas-column cases, deeper wells and heavier gases reduce surface pressure, while hotter gas columns preserve more pressure at the wellhead.