WHP to HP Calculator

How crank and wheel horsepower relate

Horsepower can be measured in two places. An engine dynamometer measures it at the crankshaft, with the engine out of the car: that is crank horsepower, also called flywheel or brake horsepower (bhp), and it is the figure engine makers rate. A chassis dynamometer measures it at the tires, with the car strapped down and its driven wheels turning a roller: that is wheel horsepower (whp). Everything in between, the transmission, driveshaft, differential, axles and the tires themselves, takes a share, and that share is the drivetrain loss.

The calculator works in both directions. As a wheel horsepower calculator, a crank to wheel horsepower calculator or a bhp to whp calculator, it takes the crank figure down to the wheels; as a crank horsepower calculator, it takes a dyno sheet back up to an estimated engine figure. The third tab, the drivetrain loss calculator, finds the percentage when you have both numbers.

What to enter and where to find it

• Wheel horsepower. The peak figure from the chassis dyno sheet. Use the corrected number and note which correction standard the sheet used, because different standards give different numbers for the same pull.
• Crank horsepower. An engine dyno result or the maker's rating. Factory ratings in the US are SAE net horsepower, an engine dyno figure corrected to standard conditions. An engine dyno run often uses different headers or exhaust, a different accessory drive and cooler intake air than the engine has in the car, so compare like with like.
• Drive layout and transmission. They pick the typical chassis-dyno loss. All-wheel drive loses the most and front-wheel drive the least; with the same layout an automatic loses more than a manual, mainly through its torque converter, and a dual-clutch box sits near the low end of the automatic range.
• Drivetrain loss. Leave it empty to use the typical chassis-dyno loss, which the results show, or type your own if you have measured the car both ways.

Why drivetrain loss isn't a fixed percentage

Quoting the loss as a percentage is a convenient rule of thumb, not physics. Transmission engineers split the losses into two kinds: load-dependent losses, mainly friction in the gear teeth and bearings, which grow with the torque going through, and load-independent losses such as oil churning, seals and pumps, which are there even with no load at all. The real loss is part fixed and part proportional.

That has a practical consequence. Because part of the loss stays roughly the same as power rises, one fixed percentage tends to overstate the loss of a high-power build and to understate it for a mild one. Efficiency also changes with the gear, the speed and the oil temperature, and a hypoid ring and pinion, with its sliding tooth contact, loses noticeably more than the spur and helical gears inside a gearbox.

The dyno adds its own spread. Chassis dynos measure in different ways, strap tension changes how the tire meets the roller, and each correction standard brings the result to its own reference weather, so the same car can read differently on two dynos or on two days. Compare figures from the same dyno, and treat any crank figure worked back from the wheels as an estimate with a range, which is why the calculator shows one.

Why a chassis dyno shows more loss than the gearbox

A chassis dyno measures power after everything between the flywheel and the roller, so it always shows more loss than the gearbox and axle alone. The driven tires flex as they roll on the drum, more on a small roller than on a flat road and more again with the car strapped down hard. Tires are labelled with rolling resistance coefficients of about 6.5 to 10.5 N per kN of load, measured on a large test drum; for a driven axle carrying 1,800 lb at 120 mph that is already 4–6 hp, before the roller's curvature, the strap-down force and the tire slipping under full torque add to it. Universal joints, CV joints and wheel bearings take a little more. An automatic's torque converter slips during a pull unless it locks, and on an inertia dyno part of the engine's power goes into speeding up the wheels, tires, driveshaft and gears during the sweep, which the dyno counts as loss: the quicker the sweep, the bigger that share. The type of dyno matters too: inertia, load-bearing and hub dynos, which bolt to the hubs and skip the tires, read the same car differently. The old shop rule that a fifth to a quarter of the power never reaches the wheels dates from heavier drivetrains, automatics without lock-up converters and older dynos; on a modern car it overstates the loss, and a crank figure worked back with it comes out too high.

WHP to HP formulas

All three tabs use the same definition: the loss is a share of crank power, written as a decimal fraction in the formulas below.

1. Crank hp = wheel hp ÷ (1 − loss)
2. Wheel hp = crank hp × (1 − loss)
3. Drivetrain loss = (crank hp − wheel hp) ÷ crank hp
4. Power lost (hp) = crank hp − wheel hp

Note the division in the first formula. Multiplying wheel hp by (1 + loss) looks similar but always comes out low, because the loss is a share of the bigger, crank figure. The range under each result repeats the calculation with the low and high ends of the typical chassis-dyno loss for your layout, so read it as the spread chassis dynos commonly show rather than as a measurement.

Worked example

Three typical questions, worked out with the same functions that run the calculator.

Typical drivetrain loss by layout

The first column is the typical chassis-dyno loss the calculator uses: the share of crank power a chassis dyno usually shows as missing, tires and joints included. A rear-wheel-drive car with a manual typically loses about 15%, anywhere from 10 to 20%; with an automatic it is about 18%, and a dual-clutch box sits near the low end of the automatic range at 16%. The last two columns show what each typical loss does to 400 crank hp and to 300 wheel hp, with the range in brackets.

The second column, the gearbox and axle alone, is secondary component data: published efficiencies multiplied together. A transmission engineering paper gives 92–97% for a passenger-car manual gearbox, 90–95% for automatic and dual-clutch boxes, 90–93% for a hypoid ring and pinion and 99–99.8% for a plain gear stage, so a rear-wheel-drive manual loses 10–17%, typically 14%, in its gearbox and axle. The gap between the two columns is the tires, joints, converter slip and the dyno itself. When you have measured your own car both ways, type that figure in instead.

All-wheel drive loses the most with any gearbox: the power goes through a transfer case or power take-off, a second differential, more shafts and four tires on the rollers, so its typical loss sits above rear-wheel drive with the same transmission, about 18% with a manual and 21% with an automatic. Front-wheel-drive transaxles skip the driveshaft and the right-angle hypoid gear, which is why their losses are the lowest, around 11% with a manual and 13% with an automatic. Inertia-type and load-bearing chassis dynos can also read the same car several percent apart, which moves the apparent loss by as much.

Common mistakes

• Multiplying instead of dividing. Wheel hp × (1 + loss) underestimates crank hp. Divide by (1 − loss), as the calculator does.
• Comparing numbers from different dynos. Two dynos, or two correction standards, can disagree on the same car. Compare before-and-after pulls on the same dyno, on the same day if you can.
• Treating the estimate as a measurement. A crank figure worked back from the wheels carries all the uncertainty of the loss percentage. Quote it with its range.
• Using one percentage at every power level. Part of the loss is fixed, so a percentage that fits a stock engine overstates the loss after a big power increase.
• Using the old shop rule on a modern car. Taking a fifth to a quarter off every dyno figure overstates the loss of a modern drivetrain and inflates the crank figure worked back from the sheet. Start from the typical chassis-dyno loss for your layout instead.
• Mixing figures from different pulls. Compare peak with peak, each taken from a full pull (on the chassis dyno, in the gear closest to 1:1). Taking a wheel figure from one pull and a crank figure from another makes the loss look larger or smaller than it is.
• Blaming the drivetrain for setup differences. An engine dyno figure taken with open headers, no accessories or cold intake air, set against a chassis dyno figure with the full exhaust, accessories and stock intake, inflates the apparent drivetrain loss. Only the gearbox, shafts, axle and tires belong in it.
• Feeding wheel hp into formulas that expect flywheel hp. Dragstrip estimates such as the quarter mile calculator are built on flywheel horsepower, so convert a dyno figure here first.