Hand Arm Vibration A8 Calculator

Purpose and model boundary

This model combines up to 12 task-specific hand-arm vibration exposures into the daily eight-hour energy-equivalent exposure A(8), HSE exposure points, threshold utilization, and a dominant-task result. It expects measured or otherwise defensible total frequency-weighted vibration magnitudes; it does not supply tool or manufacturer vibration data.

Inputs and units

Each complete row contains a task label, representative total frequency-weighted vibration magnitude a_hv in m/s², and daily trigger time in hours. UK/EU mode uses an action value of 2.5 m/s² A(8) and a limit value of 5 m/s² A(8). Custom mode uses the two positive user-entered thresholds, with the action value required to be below the limit value.

If orthogonal axes are the source measurements, their root-sum-of-squares total must be calculated before entry. For a two-handed tool, the higher-hand total is entered rather than combining exposures across hands.

Governing relationships

For task i, the workbook's squared-acceleration time contribution normalized to eight hours is:

d_i = a_hv,i² × t_i / 8

The daily exposure is:

A(8) = sqrt(Σ d_i)

The workbook's author-defined sensitivity result is:

A(8)_sensitivity = 1.20 × A(8)

HSE exposure points remain tied to the fixed UK convention even when custom thresholds are selected:

points_i = 16 × d_i = 2 × a_hv,i² × t_i

total points = Σ points_i = 100 × [A(8) / 2.5]²

Threshold utilization is calculated separately as A(8) divided by the active action or limit value. The dominant task is the first task having the greatest d_i; its contribution share is max(d_i) / Σd_i, or zero when total dose is zero.

Calculation sequence

1. Validate threshold profile, complete task rows, nonnegative magnitudes, nonnegative trigger times, and total daily trigger time.
2. Require at least one active task and at least one task with positive duration; unused table rows remain excluded.
3. Calculate each task's normalized dose and fixed-convention exposure points.
4. Sum dose, take its square root for A(8), and calculate the +20% sensitivity value.
5. Compare the result with active thresholds, identify the dominant task, and evaluate status in the order below.

Outputs and interpretation

A(8) is the principal daily energy-equivalent result. Exposure points provide the HSE convention of 100 points at the UK action value and 400 points at the UK limit value. Custom thresholds alter utilization and classification, but do not redefine those points. The +20% result is a near-threshold sensitivity check, not a statistical confidence bound or a claimed measurement-uncertainty interval.

Validation and status logic

This is the exact precedence of the workbook Model_Status formula; duplicate labels take precedence over threshold classification.

Assumptions and limitations

• Entered a_hv values are representative total frequency-weighted hand-arm vibration values for the assessed worker and process.
• Daily trigger times do not overlap and sum to no more than 24 hours.
• Measurement setup, axis weighting, mounting correction, representativeness, and uncertainty assessment are outside scope.
• Actual exposure can vary materially among workers, tools, workpieces, and operating conditions.
• The +20% sensitivity is an author-defined caution based on commonly cited measurement variability; it is not a prescribed uncertainty bound.
• The workbook contains no HSE tool lookup values, ISO weighting curves, manufacturer data, or licensed measurement tables.
• The 1,000 m/s² magnitude ceiling is a calculation guardrail, not an exposure recommendation.

Restrictions and non-computing states

All 12 task slots must be either unused or contain a complete valid row. Active labels are limited by the workbook, magnitudes and times cannot be negative, at least one trigger time must be positive, and total trigger time cannot exceed 24 hours. In custom mode both thresholds must be positive and the action threshold must be strictly lower than the limit threshold.

Errors and warnings

NOT VALID blocks interpretation of the exposure outputs. CHECK identifies duplicate labels, a threshold reached by the central estimate, or a near-threshold sensitivity result. A publishing, connection, or calculation-service error is not a vibration classification.

The task-dose formula, point conversion, +20% sensitivity, active-threshold logic, restrictions, and exact status precedence were traced through the delivered workbook and checked against its published input rules, tests, and reviewer packet. The workbook identifies these technical sources:

• HSE L140 — Hand-arm vibration — Daily A(8), vector-sum vibration, action and limit values, exposure points, and assessment cautions.
• HSE hand-arm vibration calculator guide — Multi-task exposure-point addition and eight-hour daily exposure interpretation.
• Control of Vibration at Work Regulations 2005 — Legal action and limit values and the eight-hour reference period.
• EU Directive 2002/44/EC — Daily action and limit values and higher-hand treatment for two-handed equipment.