Horsepower vs Torque Calculator: Gearing and Wheel Force

The calculation uses full-load crankshaft torque points. Linear interpolation gives $T(n)$ only between the first and last entered rpm points. No torque or power is extrapolated outside that interval. Derived power is

The formulas use explicit unit conversions rather than a hidden rpm factor. OpenStax, University Physics 1 §10.8 gives the rotational power relation. NIST SP 811 gives mechanical horsepower as approximately 745.7 W; this is not metric horsepower (PS, approximately 735.5 W).

For gearbox ratio $i_g$ and final drive $i_f$, the no-slip kinematics and wheel force are

Wheel torque is the sum at the driven tyres, not the torque at a single halfshaft. The tool checks all six discrete gears and chooses the greatest feasible wheel force at the selected speed. A tie selects the first eligible gear. It does not predict a shift schedule.

Road load follows NASA's drag equation and the constant rolling-coefficient model documented by MathWorks:

Here $C_dA$ is the drag coefficient times frontal area, and $g=9.80665\;\mathrm{m/s^2}$. With no slip, $F_wv=\eta P$. This identity explains why more power available at the wheels at the same speed, rather than a larger crank-torque rating by itself, gives greater acceleration for otherwise equal cars.

The peak-power table samples each interpolated curve at 241 equally spaced rpm values. The exact peak can lie between samples. The crossover plot shows the dimensionless ratios $P/(1\;\mathrm{hp})$ and $T/(1\;\mathrm{lb\!\cdot\!ft})$ on one numerical scale; their nonzero intersection occurs at approximately 5,252.1 rpm. It intentionally keeps those units even when physical result cards and charts use metric display.

Holley's Hot Rod Calc guide provides independent worked checks: attached PDF p.50 (printed p.48) for both converter directions, p.43 for road speed, and p.44 for cruising rpm. Tolerances allow the guide's three-decimal rounding. OpenStax Example 10.19 independently checks the inverse relation. Short quotes in the verification cases identify the published results.

Animation uses closed-form wheel and crank angles from the current speed and selected gear. Time affects only those angles, scrolling road marks and the schematic; dyno sweeps and gear selection do not depend on animation time.

The dyno plotting axis is the sorted union of both engines' individual sampling grids and all entered rpm points. Each engine retains its own samples even when its usable rpm interval is very narrow. Values outside its entered interval remain explicit chart gaps.

• Engine A and B defaults are author-designed teaching curves. They are editable inputs, not measured dyno data or manufacturer claims.
• All entered torques refer to the crankshaft under full load. A chassis-dyno trace requires a separate, justified conversion before use.
• Both cars have identical mass, tyre diameter, constant drivetrain efficiency, drag area and rolling coefficient; only the entered engine curves and final drives differ.
• Rigid, no-slip gearing; fixed effective rolling radius; still air; level road; constant air density and rolling coefficient. Vehicle speed is positive.
• Translational mass only: wheel, shaft, flywheel and engine rotational inertia are omitted. No tyre traction limit, load transfer, turbo lag, clutch slip, torque converter, rev-limiter dynamics, gearshift loss or accessory-load map.
• The five entered rpm points delimit the usable range. Gaps mean unavailable rpm data, not zero measured engine torque.
• The 538 W human scale is OpenStax College Physics 2e Example 7.11, a brief stair-running example. The one-horsepower horse benchmark follows that text's sustained-work comparison and is a scale reference, not a fixed maximum power for every horse. Donut's video illustrates why actual horse output and test duration matter.
• Drawings are schematic; force arrows share a normalized scale and the drawing's speed annotation is in km/h. Wheels and crank markers move at 1/40 real time. Animation never integrates an acceleration history.

Use this for teaching, dimensional checks and preliminary comparisons of full-load torque curves. Enter five strictly increasing rpm values for each engine and positive, descending transmission ratios. At least one positive torque point and at least one usable gear at the selected speed are required for each engine. Adjust the speed, final drive, ratios or curve endpoints when the input message says no gear is available.

The single-point converter and gearing probe are independent of the dyno curves. The probe uses engine A's final drive; its reported speed may exceed the usable engine range because it is a kinematic conversion, not a speed prediction.

The force envelope is an instantaneous, traction-unlimited result. It cannot establish launch performance, safe vehicle speed, passing distance, quarter-mile elapsed time or a real shift strategy. A force curve above road load indicates positive acceleration only under the stated assumptions. A sampled peak-power rating can miss a narrow peak, especially with irregularly spaced user points.

The normal metric/US controls convert physical inputs, result cards, tables and chart axes. The crossover plot is deliberately dimensionless and labelled in fixed numerical hp/lb-ft units. It must not be interpreted as equality between physical torque and power.

Full-run simulations belong in the separate Quarter-Mile and 0–60 Simulator. That companion is not currently available in the catalog. This explorer does not predict complete runs.

The crossover is visible only when engine B's entered rpm interval contains approximately 5,252 rpm and torque there is nonzero. Changing a curve does not preserve the default engine's high-torque or high-revving character.