Reconcile one completed positive-demand bicycle interval from source-owned speed, grade, wind, coefficients, drivetrain efficiency, and crank power.
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Inputs that matter
One de-identified completed owner, mechanic/coach or reviewed-test positive-demand steady-state bicycle interval; responsible record/revision/date/reviewer; exact bicycle/load/interval; rider/bicycle/clothing/carried-load and position records; wheel/tire/pressure/load/surface state; completed ground-speed, signed rise/run grade and signed longitudinal-wind sources; source-owned air density, CdA, Crr, crank-to-wheel efficiency and other positive resistance; steady-state boundary; crank-power installation/calibration and same-interval synchronization/averaging/zero semantics; tolerance/disposition, safety and retention records; bounded entered values; a completed crank-power report; and an optional same-interval independent source plus crank power
Output to expect
Ground and relative-air speeds, resolved slope angle, gravity/rolling/aerodynamic/other forces and powers, total wheel force and power, entered-efficiency drivetrain loss, reproduced crank demand, completed signed difference, plus optional independent signed differences
How it works
Validate every provenance field and bounded value; convert ground speed to m/s; require positive relative airflow from ground speed plus signed headwind; convert rise/run grade with atan; use NIST standard gravity; reproduce gravity as m·g·sin(theta), rolling force as m·g·Crr·cos(theta), and aerodynamic force as one-half density·CdA·relative-air-speed squared; add only the entered nonnegative other force; multiply by ground speed; require positive wheel demand; divide by entered efficiency; enforce the user-owned tolerance for completed and optional reports; require optional source/power together; and normalize only mathematical zero
Confirm that total moving mass, exact bicycle/load, rider position/clothing, wheel/tire/pressure/surface, speed, grade, longitudinal wind, air density, CdA, Crr, drivetrain efficiency, other resistance, power-meter location/calibration, start/stop interval, averaging and zero semantics all match. Another state, method, interval or source revision needs another run.
Use the result only for one completed positive-demand steady-state force-balance and transcription check. It does not infer inputs; model acceleration, rotating inertia, crosswind/yaw, gusts, drafting, tire slip, rider movement, motor assist, braking, coasting, regeneration or nonpositive demand; validate instruments, installation, condition or safety; estimate FTP, physiology, performance or training; choose equipment; diagnose discrepancies; or authorize service, purchase or riding.
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Built around the job you need to finish
Reconcile one completed synchronized positive-demand steady-state bicycle interval from source-owned mass, ground speed, signed grade and longitudinal wind, air density, CdA, Crr, drivetrain efficiency, other resistance and crank-power reports without estimating FTP, predicting performance or prescribing power.
Mechanic auditing one controlled power interval
Replace silent generic aerodynamic, rolling and drivetrain constants with exact same-state records and transparent force components.
Freeze the bicycle, load, position, wheel/tire/surface, environment and interval, then enter source-owned speed, grade, wind, coefficients, efficiency and crank-power evidence.
Receives reproducible wheel and crank demand plus signed agreement evidence while calibration, installation, condition, service and safety decisions remain external.
Coach reviewing interval synchronization
Prevent power, speed, grade, wind or coefficient observations from different intervals or averaging rules from being treated as one controlled record.
Retain matching start/stop time, arithmetic or device averaging, zero inclusion, measurement locations, rider position and environmental state for every input.
Can identify an arithmetic or transcription mismatch without receiving an FTP, pacing, training, physiology or performance recommendation.
Owner documenting an unexplained meter difference
Avoid blaming the power meter, tires, wind, grade, drivetrain or rider position from an under-specified estimate.
Record source revisions, calibration, exact configuration, coefficients, user-owned tolerance and responsible reviewer, then optionally add one independent same-interval report.
Gets transparent component powers and a clear escalation boundary rather than an unsupported diagnosis, equipment choice or permission to ride.
Authoritative checks for this tool
Outputs and checklists are planning aids. Review the linked current authorities and the records, terms, instructions, and requirements that apply to your exact situation before a consequential decision.
Retain one bicycle, moving load, rider position, wheel/tire/pressure/surface state, environment, start/stop interval, averaging rule, zero treatment, coefficient basis, and crank-power source. Another state, interval, source revision, position, tire pressure, surface, or wind condition needs another record.
Resolve source-owned longitudinal forces
Convert rise/run grade to an angle with arctangent. Apply the entered same-state Crr to the normal-force component and the entered CdA and air density to positive relative airflow. No coefficient or atmosphere constant is silently supplied.
F = m·g·sin(atan(grade/100)) + m·g·Crr·cos(atan(grade/100)) + ½·ρ·CdA·v_air² + entered other N
Reproduce wheel and crank demand
Multiply total longitudinal wheel force by ground speed, then divide positive wheel demand by the entered crank-to-wheel efficiency. The displayed drivetrain loss is arithmetic from that entered source value, not a condition diagnosis.
Compare the completed and optional independent same-interval crank-power reports against reproduced crank demand using only the tolerance owned by the completed record. An out-of-tolerance difference stops the result instead of being silently explained or corrected.
Updated: August 2026
Example Scenarios
Reproduce the completed crank-power report after confirming exact mass, setup, position, surface, grade, longitudinal wind, coefficient sources, efficiency, synchronization, and calibration evidence.
Verify that ground speed, wind, environmental inputs, coefficient applicability, zero handling, and crank power all describe the same completed steady-state interval.
Expose an arithmetic mismatch for responsible review without blaming the power meter, grade, wind, tires, drivetrain, rider position, or equipment condition from the model alone.
Common Mistakes to Avoid
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Using grade percent directly as the sine of slope angle
✓
Treat percent grade as rise divided by run × 100, resolve the slope angle with arctangent, and retain the exact source/method.
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Inserting generic CdA, Crr, air-density, or drivetrain-loss constants
✓
Use completed source-owned values applicable to the exact interval, rider position, tire/pressure/load/surface state, environment, and drivetrain measurement location.
✕
Treating arithmetic agreement as a power-meter, performance, or safety approval
✓
Keep calibration, installation, condition, discrepancy diagnosis, training, equipment, service, safety, and riding decisions with the responsible sources and reviewers.
FAQ
No. It reconciles one already completed positive-demand steady-state record. Physiology, FTP, pacing, training zones, fatigue, symptoms, performance, and targets are outside its task.
They are source-dependent properties of the retained position, equipment, surface, environment, method, and drivetrain state. A generic constant would hide the largest modeling assumptions instead of documenting them.
Enter longitudinal headwind as positive and tailwind as negative. Ground speed plus the signed wind must remain positive. Crosswind, yaw, gusts, drafting, and turbulent or rapidly changing flow are unsupported.
This record only supports positive forward wheel demand. A force balance at or below zero enters braking, coasting, regeneration, control, and transient behavior that this arithmetic does not model.
Possible causes include nonmatching intervals, averaging or zero handling, speed or grade measurement, wind and air-density basis, CdA or Crr applicability, load, drivetrain efficiency, measurement location, calibration, transcription, excluded dynamics, or condition. The Tool reports the difference but does not diagnose it.
No. Agreement does not validate installation, crank length, calibration, firmware, compatibility, condition, braking, traffic/course controls, rider readiness, compliance, or permission to ride.
About Reviewed Bicycle Steady-State Power Balance
Reproduce one completed synchronized positive-demand interval from exact source-owned mass, ground speed, rise/run grade, longitudinal wind, air density, CdA, Crr, drivetrain efficiency, other resistance, and crank-power reports. The result checks force-balance arithmetic and transcription only; it does not estimate FTP, predict performance, prescribe power, choose equipment, diagnose a discrepancy, or authorize riding.
