Drilling Formulas Cheat Sheet

Read the units before you use the number. Almost every mistake on this page's subject comes from mixing unit systems, not from getting the algebra wrong. Every formula here is in oilfield units — ppg, psi, feet, inches, barrels, gpm — and depth means true vertical depth unless it says otherwise. Pressure does not care how far you drilled sideways.

Pressure and Hydrostatics

The foundation. Everything in well control resolves back to these three lines.

Hydrostatic Pressure

HP (psi) = 0.052 × MW (ppg) × TVD (ft)

The pressure the mud column exerts at depth. TVD, never measured depth.

Pressure Gradient

Gradient (psi/ft) = 0.052 × MW (ppg)

Freshwater ≈ 0.433 psi/ft · seawater ≈ 0.444 psi/ft · overburden ≈ 1.0 psi/ft.

Equivalent Mud Weight

EMW (ppg) = P (psi) ÷ (0.052 × TVD (ft))

Converts any pressure back into the mud weight that would produce it. This is how a leak-off test result becomes a number you can compare to mud weight.

Equivalent Circulating Density

ECD (ppg) = MW (ppg) + APL (psi) ÷ (0.052 × TVD (ft))

APL = annular pressure loss. ECD always exceeds static mud weight while pumping, which is why wells are lost on connections and regained on them too.

Overbalance

Overbalance (psi) = HP − Pore Pressure

Negative overbalance is a kick in progress. Excessive overbalance is differential sticking waiting to happen.

The full treatment of these, including the mud weight window and swab and surge, is on the mud weight and hydrostatic pressure page, and you can run them against your own numbers in the hydrostatic pressure calculator.

Mud Weight Conversions

The same fluid gets reported four different ways depending on who is writing the report. These are exact, not rounded.

From ppg, multiply by	To get	12.0 ppg becomes
÷ 8.3454	Specific gravity	1.438
÷ 19.25	psi/ft	0.6234
× 7.4805	lb/ft³	89.77
× 119.826	kg/m³	1,437.9
÷ 8.5099	bar/10 m	1.410

Note that 19.25 is the exact reciprocal of the 0.052 constant — they are the same conversion written two ways, which is worth knowing when a figure looks off by a factor you cannot place. The mud weight converter does all five live.

Well Control and the Kill Sheet

Shut-in pressures are readings. These turn them into a plan.

Kill Mud Weight

KMW (ppg) = OMW (ppg) + SIDPP (psi) ÷ (0.052 × TVD (ft))

OMW = original mud weight · SIDPP = shut-in drillpipe pressure. The drillpipe is the clean gauge because it is full of known mud.

Initial Circulating Pressure

ICP (psi) = SIDPP + SCRP

SCRP = slow circulating rate pressure, recorded before the kick, not estimated during it.

Final Circulating Pressure

FCP (psi) = SCRP × (KMW ÷ OMW)

Where the drillpipe pressure should settle once kill mud reaches the bit.

Pressure Step Down the String

Step (psi/100 stk) = (ICP − FCP) ÷ (strokes to bit ÷ 100)

The schedule you hold the drillpipe pressure to while displacing the string.

MAASP

MAASP (psi) = (FG (ppg) − MW (ppg)) × 0.052 × Shoe TVD (ft)

Maximum allowable annular surface pressure. FG = fracture gradient as EMW at the shoe. Recalculate it every time mud weight changes — it moves, and people forget.

Influx Height and Density

h (ft) = Pit gain (bbl) ÷ Annular capacity (bbl/ft)
ρ (ppg) = MW − (SICP − SIDPP) ÷ (0.052 × h)

Roughly: below ~4 ppg treat it as gas, above ~7 ppg as liquid. The gap between SICP and SIDPP is what tells you.

The procedure these feed — shut in, read, circulate — is on the well control page, and the kill sheet calculator runs the whole sequence.

Capacities, Volumes and Strokes

All three capacity formulas are the same formula. Only the diameters change.

Capacity and Displacement

Pipe capacity (bbl/ft) = ID² ÷ 1029.4
Annular capacity (bbl/ft) = (D_hole² − D_pipe²) ÷ 1029.4
Displacement (bbl/ft) = (OD² − ID²) ÷ 1029.4

All diameters in inches. 1029.4 is exact to four figures — it is 9,702 in³ per barrel divided by the area constant.

Pump Output — Triplex

Output (bbl/stk) = 0.000243 × Liner ID² (in) × Stroke (in) × Efficiency

Volumetric efficiency is typically 0.95–1.00. Measure it rather than assuming it; a worn pump quietly ruins every stroke count downstream.

Strokes and Bottoms Up

Strokes = Volume (bbl) ÷ Pump output (bbl/stk)

Strokes to bit uses drill string capacity. Bottoms up uses annular volume. Total circulation is both.

Annular Velocity

AV (ft/min) = 24.5 × Q (gpm) ÷ (D_hole² − D_pipe²)

The number that decides whether cuttings come out. Hole cleaning fails in high-angle sections long before AV looks bad on paper.

Why hole cleaning stops obeying annular velocity past about 30° is covered in hole cleaning in high-angle wells.

Buoyancy and String Weight

Buoyancy Factor

BF = 1 − (MW (ppg) ÷ 65.5)

Buoyed weight = air weight × BF. At 12 ppg, BF ≈ 0.817, so a string loses about 18% of its weight.

A note on 65.5: steel at 489.5 lb/ft³ works out at 65.44 ppg, not 65.5. The rounded figure is the field convention and the difference is under a tenth of a percent, but if a number will not reconcile against a supplier's tally book, this is one of the places the discrepancy hides.

Neutral Point

Max WOB (lb) = Collar weight (lb/ft) × Length (ft) × BF

Keep the neutral point in the collars. Putting drill pipe in compression is how you buy a fatigue failure.

Pipe grades, inspection classes and where the neutral point should sit are on the drill string page.

Directional and Survey

TVD over a Constant-Inclination Section

ΔTVD (ft) = ΔMD (ft) × cos I

I = inclination from vertical. In a build section use minimum curvature rather than this.

Build Rate

Build rate (°/100 ft) = (I₂ − I₁) × 100 ÷ Course length (ft)

Inclination change only. It is not the same as dogleg severity unless azimuth is constant.

Dogleg Severity

cos β = cos(I₂ − I₁) − sin I₁ × sin I₂ × (1 − cos(A₂ − A₁))
DLS (°/100 ft) = β × 100 ÷ Course length (ft)

The minimum curvature dogleg angle β, accounting for both inclination and azimuth change. When azimuth is unchanged it collapses to the build rate above.

Well profiles, build sections and why dogleg severity limits matter are on the directional drilling page.

The Constants, and Where They Come From

Every rounded constant on this page is a unit conversion, not a fudge factor. Knowing the derivation is what lets you rebuild one when a figure looks wrong.

Constant	Exact value	What it is
0.052	0.0519481	12 ÷ 231 — cubic inches per foot of a 1 in² column, over cubic inches per gallon
19.25	19.25	Exactly 1 ÷ 0.0519481. The same conversion inverted
1029.4	1029.4142	Barrel volume ÷ area constant, giving bbl per foot from inches squared
24.5	24.5099	gpm to ft/min through an annulus measured in inches
0.000243	0.00024286	Three cylinders, per stroke, expressed in barrels
8.3454	8.345404	Pounds per gallon of fresh water — the specific gravity anchor
1 bbl	42 gal = 5.6146 ft³	9,702 cubic inches

One Worked Example, End to End

A 12.0 ppg mud at 10,000 ft TVD. The well kicks and is shut in on 400 psi drillpipe, 550 psi casing, with a 12 bbl pit gain in a 8½ in hole around 5 in pipe.

Hydrostatic: 0.052 × 12.0 × 10,000 = 6,240 psi
Formation pressure: 6,240 + 400 = 6,640 psi
Kill mud weight: 12.0 + 400 ÷ (0.052 × 10,000) = 12.0 + 0.77 = 12.77 ppg, call it 12.8
Annular capacity: (8.5² − 5²) ÷ 1029.4 = (72.25 − 25) ÷ 1029.4 = 0.0459 bbl/ft
Influx height: 12 ÷ 0.0459 = 261 ft
Influx density: 12.0 − (550 − 400) ÷ (0.052 × 261) = 12.0 − 11.05 = 0.95 ppg — gas

That last line is the one that changes the shift. A 0.95 ppg influx is gas, gas migrates, and a gas kick shut in on a well that is not being circulated will carry its pressure to surface whether or not anyone is watching the gauges. The arithmetic took a minute; the conclusion decides what happens for the next twelve hours.

These are the standard field equations, not a substitute for your well programme. Rig-specific procedures, your operator's well control policy and the standard governing your jurisdiction take precedence over anything on this page. Check pump output by measurement, check slow circulating rates on tour, and verify fracture gradient against the actual leak-off test rather than a gradient assumption.

Drilling Formulas Cheat Sheet

Pressure and Hydrostatics

Mud Weight Conversions

Well Control and the Kill Sheet

Capacities, Volumes and Strokes

Buoyancy and String Weight

Directional and Survey

The Constants, and Where They Come From

One Worked Example, End to End

🧮 Run the Numbers

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